[ { "path": ".gitattributes", "content": "# Auto detect text files and perform LF normalization\n* text=auto\n\n# Custom for Visual Studio\n*.cs diff=csharp\n\n# Standard to msysgit\n*.doc\t diff=astextplain\n*.DOC\t diff=astextplain\n*.docx diff=astextplain\n*.DOCX diff=astextplain\n*.dot diff=astextplain\n*.DOT diff=astextplain\n*.pdf diff=astextplain\n*.PDF\t diff=astextplain\n*.rtf\t diff=astextplain\n*.RTF\t diff=astextplain\n" }, { "path": ".gitignore", "content": "# Windows image file caches\nThumbs.db\nehthumbs.db\n\n# Folder config file\nDesktop.ini\n\n# Recycle Bin used on file shares\n$RECYCLE.BIN/\n\n# Windows Installer files\n*.cab\n*.msi\n*.msm\n*.msp\n\n# Windows shortcuts\n*.lnk\n\n# =========================\n# Operating System Files\n# =========================\n\n# OSX\n# =========================\n\n.DS_Store\n.AppleDouble\n.LSOverride\n\n# Thumbnails\n._*\n\n# Files that might appear on external disk\n.Spotlight-V100\n.Trashes\n\n# Directories potentially created on remote AFP share\n.AppleDB\n.AppleDesktop\nNetwork Trash Folder\nTemporary Items\n.apdisk\n" }, { "path": ".ipynb_checkpoints/Bayes' Theorem-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"source\": [\n \"# Bayes Theorem\\n\",\n \"\\n\",\n \"In this Statistics Notebook we will be going over Bayes Theorem and an example of how to use it. This theorem will be important to understand in many situations and we will be using it for Machine Learning in certain lectures.\\n\",\n \"\\n\",\n \"We will start by describing the equation for Bayes Theorem and then complete an example problem. There won't be a SciPy portion to this lecture because this is really more of a math overview than a discussion on a distribution.\\n\",\n \"\\n\",\n \"### Overview\\n\",\n \"\\n\",\n \"In probability theory and statistics, Bayes' theorem describes the probability of an event, based on conditions that might be related to the event. Bayes Theorem allows us to use previously known information to asess likelihood of another related event.\\n\",\n \"\\n\",\n \"You will usually see Bayes Theorem displayed in one of two ways:\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B)} $$\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B|A)P(A) + P(B|not A)P(not A)}$$\\n\",\n \"\\n\",\n \"Here P(A|B) stands for the Probability that A happened given B has occured. These are both the same, in the second case, you would use this form if you don't directly have the Probability of B occuring on its own.\\n\",\n \"\\n\",\n \"Let's go ahead and dive into an example Problem to see how to use Baye's Theorem!\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Example Problem\\n\",\n \"\\n\",\n \"This is a classic example of Bayes Theorem:\\n\",\n \"\\n\",\n \"We have a test to screen for breast cancer, with the following conditions:\\n\",\n \"\\n\",\n \"- 1% of women have breast cancer \\n\",\n \"- 80% of mammograms detect breast cancer when it is there\\n\",\n \"- 9.6 % of mammograms detect breast cancer when it is *not* there. (False Positive)\\n\",\n \"\\n\",\n \"We could assign the probabilities to the sample space by using a table:\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"
Cancer (1%)No Cancer (99%)
Tested Positive80%9.6%
Tested Negative20%90.4%
\\n\",\n \"\\n\",\n \"\\n\",\n \"Now let's say you wanted to know how accurate this test is. If someone went to go get the test and had a positive result, what is the probability that they have breast cancer?\\n\",\n \"\\n\",\n \"We can first visualize Bayes Theorem by filling out the table above:\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"
Cancer (1%)No Cancer (99%)
Tested PositiveTrue Positive: 1% × 80%False Positive: 99% × 9.6%
Tested NegativeFalse Negative: 1% × 20%True Negative: 99% × 90.4%
\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Remember that the proabbility of an event occuring is the number of ways it could happen given all possible outcomes:\\n\",\n \"\\n\",\n \"$$ Probability = \\\\frac{Desired \\\\ event} { All \\\\ possibilities}$$\\n\",\n \"\\n\",\n \"Then the probability of getting a real, positive result is .01 × .8 = .008. \\n\",\n \"\\n\",\n \"The chance of getting any type of positive result is the chance of a *true positive* plus the chance of a *false positive* \\n\",\n \"which is (.008 + 0.09504 = .10304).\\n\",\n \"\\n\",\n \"So, our chance of cancer is .008/.10304 = 0.0776, or about 7.8%.\\n\",\n \"\\n\",\n \"This means that a positive mammogram results in only a 7.8% chance of cancer, rather than 80% (the supposed accuracy of the test). \\n\",\n \"\\n\",\n \"This might seem counter intuitive at first but it makes sense: the test gives a false positive 10% of the time, so there will be a ton of false positives in any given population. There will be so many false positives, in fact, that most of the positive test results will be wrong.\\n\",\n \"\\n\",\n \"Now we can turn the above process into the Bayes Theorem Equation:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's go ahead and plug in the information we do know into the second equation.\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B|A)P(A) + P(B|not A)P(not A)}$$\\n\",\n \"\\n\",\n \"Looking back on the information we were given:\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(A|B) = Chance of having cancer (A) given a positive test (B). This is the desired information: How likely is it to have cancer with a positive result? We've already solved it using the table, so let's see if the equation agrees with our results: 7.8%.\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(B|A) = Chance of a positive test (B) given that you had cancer (A). This is the chance of a true positive, 80% in this case.\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(A) = Chance of having cancer (1%).\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(not A) = Chance of not having cancer (99%).\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(B|not A) = Chance of a positive test (B) given that you didn’t have cancer ( Not A). This is a false positive, 9.6% in our case.\\n\",\n \"\\n\",\n \"Plugging in these numbers, we arrive at the same answer as our table method: 7.76%\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Other great resources for more on Bayes Theorem:\\n\",\n \"\\n\",\n \"1.) [Simple Explanation using Legos](https://www.countbayesie.com/blog/2015/2/18/bayes-theorem-with-lego)\\n\",\n \"\\n\",\n \"2.) [Wikipedia](http://en.wikipedia.org/wiki/Bayes%27_theorem)\\n\",\n \"\\n\",\n \"3.) [Stat Trek](http://stattrek.com/probability/bayes-theorem.aspx)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Bayseian A-B Testing-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Beta Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"####Let's learn the Beta distribution!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true\n },\n \"source\": [\n \"The beta distribution is a continuous distribution which can take values between 0 and 1. This distribution is parameterized by \\n\",\n \"two shape parameters α and β.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"import seaborn as sns\\n\",\n \"\\n\",\n \"from scipy import stats\\n\",\n \"\\n\",\n \"a = 0.5\\n\",\n \"b = 0.5\\n\",\n \"x = np.arange(0.01,1,0.01)\\n\",\n \"y = stats.beta.pdf(x,a,b)\\n\",\n \"plt.plot(x,y)\\n\",\n \"plt.title('Beta: a=%.1f,b=%.1f' %(a,b))\\n\",\n \"\\n\",\n \"plt.xlabel('x')\\n\",\n \"plt.ylabel('Probability density')\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Binomial Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Binomial is a specific type of a discrete probability distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's see an example question first, and then learn about the binomial distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Example 1: Two players are playing basketball, player A and player B. Player A takes an average of 11 shots per game, and \\n\",\n \"has an average success rate of 72%. Player B takes an average of 15 shots per game, but has an average success rate of 48%.\\n\",\n \"\\n\",\n \"Question 1: What's the probability that Player A makes 6 shots in an average game?\\n\",\n \"\\n\",\n \"Question 2: What's the probability that Player B makes 6 shots in an average game?\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can classify this as a binomial experiment if the following conditions are met:\\n\",\n \" \\n\",\n \" 1.) The process consists of a sequence of n trials.\\n\",\n \" 2.) Only two exclusive outcomes are possible for each trial (A success and a failure)\\n\",\n \" 3.) If the probability of a success is 'p' then the probability of failure is q=1-p\\n\",\n \" 4.) The trials are independent.\\n\",\n \" \\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The formula for a Binomial Distribution Probability Mass Function turns out to be: \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$Pr(X=k)=C(n,k)p^k (1-p)^{n-k}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where n= number of trials,k=number of successes,p=probability of success,1-p=probability of failure (often written as q=1-p).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that to get exactly 'k' successes in 'n' trials, we want exactly 'k' successes: $$p^k$$ \\n\",\n \"and we want 'n-k' failures:$$(1-p)^{n-k}$$\\n\",\n \"Then finally, there are $$C(n,k)$$ ways of putting 'k' successes in 'n' trials.\\n\",\n \"So we multiply all these together to get the probability of exactly that many success and failures in those n trials!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"--------------------------------------------------------------------------------------------------------------------------------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Quick note, C(n,k) refers to the number of possible combinations of N things taken k at a time.\\n\",\n \"\\n\",\n \"This is also equal to: $$C(n,k) = \\\\frac{n!}{k!(n-k)!}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### So let's try out the example problem!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" The probability of player A making 6 shots in an average game is 11.1% \\n\",\n \" \\n\",\n \"\\n\",\n \" The probability of player B making 6 shots in an average game is 17.0% \\n\"\n ]\n }\n ],\n \"source\": [\n \"# Set up player A\\n\",\n \"\\n\",\n \"# Probability of success for A\\n\",\n \"p_A = .72\\n\",\n \"# Number of shots for A\\n\",\n \"n_A = 11\\n\",\n \"\\n\",\n \"# Make 6 shots\\n\",\n \"k = 6\\n\",\n \"\\n\",\n \"# Now import scipy for combination\\n\",\n \"import scipy.special as sc\\n\",\n \"\\n\",\n \"# Set up C(n,k)\\n\",\n \"comb_A = sc.comb(n_A,k)\\n\",\n \"\\n\",\n \"# Now put it together to get the probability!\\n\",\n \"answer_A = comb_A * (p_A**k) * ((1-p_A)**(n_A-k))\\n\",\n \"\\n\",\n \"# Put the answer in percentage form!\\n\",\n \"answer_A = 100*answer_A\\n\",\n \"\\n\",\n \"\\n\",\n \"# Quickly repeat all steps for Player B\\n\",\n \"p_B = .48\\n\",\n \"n_B = 15\\n\",\n \"comb_B = sc.comb(n_B,k)\\n\",\n \"answer_B = 100 * comb_B * (p_B**k) * ((1-p_B)**(n_B-k))\\n\",\n \"\\n\",\n \"\\n\",\n \"#Print Answers\\n\",\n \"print( ' The probability of player A making 6 shots in an average game is %1.1f%% ' %answer_A)\\n\",\n \"print( ' \\\\n')\\n\",\n \"print( ' The probability of player B making 6 shots in an average game is %1.1f%% ' %answer_B)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now we know that even though player B is technically a worse shooter, because she takes more shots she will have a higher chance of making 6 shots in an average game!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"But wait a minute... what about a higher amount of shots, will player's A higher probability take a stronger effect then?\\n\",\n \"What's the probability of making 9 shots a game for either player?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 44,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" \\n\",\n \"\\n\",\n \" The probability of player A making 9 shots in an average game is 22.4% \\n\",\n \"\\n\",\n \"\\n\",\n \" The probability of player B making 9 shots in an average game is 13.4% \\n\",\n \"\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"#Let's find out!\\n\",\n \"\\n\",\n \"#Set number of shots\\n\",\n \"k = 9\\n\",\n \"\\n\",\n \"#Set new combinations\\n\",\n \"comb_A = sc.comb(n_A,k)\\n\",\n \"comb_B = sc.comb(n_B,k)\\n\",\n \"\\n\",\n \"# Everything else remains the same\\n\",\n \"answer_A = 100 * comb_A * (p_A**k) * ((1-p_A)**(n_A-k))\\n\",\n \"answer_B = 100 * comb_B * (p_B**k) * ((1-p_B)**(n_B-k))\\n\",\n \"\\n\",\n \"#Print Answers\\n\",\n \"print( ' \\\\n')\\n\",\n \"print( ' The probability of player A making 9 shots in an average game is %1.1f%% ' %answer_A)\\n\",\n \"print( '\\\\n')\\n\",\n \"print( ' The probability of player B making 9 shots in an average game is %1.1f%% ' %answer_B)\\n\",\n \"print( '\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we see that player's A ability level gives better odds of making exactly 9 shots. We need to keep in mind that we are asking\\n\",\n \"about the probability of making *exactly* those amount of shots. This is a different question than \\\" What's the probability that player A makes *at least* 9 shots?\\\".\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Now let's investigate the mean and standard deviation for the binomial distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean of a binomial distribution is simply: $$\\\\mu=n*p$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This intuitively makes sense, the average number of successes should be the total trials multiplied by your average success rate.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Similarly we can see that the standard deviation of a binomial is: $$\\\\sigma=\\\\sqrt{n*q*p}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now we can ask, whats the average number of shots each player will make in a game +/- a standard distribution?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 52,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\n\",\n \"\\n\",\n \"Player A will make an average of 8 +/- 1 shots per game\\n\",\n \"\\n\",\n \"\\n\",\n \"Player B will make an average of 7 +/- 2 shots per game\\n\",\n \"\\n\",\n \"\\n\",\n \"NOTE: It's impossible to make a decimal of a shot so '%1.0f' was used to replace the float!\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Let's go ahead and plug in to the formulas.\\n\",\n \"\\n\",\n \"# Get the mean\\n\",\n \"mu_A = n_A *p_A\\n\",\n \"mu_B = n_B *p_B\\n\",\n \"\\n\",\n \"#Get the standard deviation\\n\",\n \"sigma_A = ( n_A *p_A*(1-p_A) )**0.5\\n\",\n \"sigma_B = ( n_B *p_B*(1-p_B) )**0.5\\n\",\n \"\\n\",\n \"# Now print results\\n\",\n \"print( '\\\\n')\\n\",\n \"print( 'Player A will make an average of %1.0f +/- %1.0f shots per game' %(mu_A,sigma_A))\\n\",\n \"print( '\\\\n')\\n\",\n \"print( 'Player B will make an average of %1.0f +/- %1.0f shots per game' %(mu_B,sigma_B))\\n\",\n \"print( '\\\\n')\\n\",\n \"print( \\\"NOTE: It's impossible to make a decimal of a shot so '%1.0f' was used to replace the float!\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's see how to automatically make a binomial distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 60,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"7.92\\n\",\n \"1.4891608375189027\\n\"\n ]\n }\n ],\n \"source\": [\n \"from scipy.stats import binom\\n\",\n \"\\n\",\n \"# We can get stats: Mean('m'), variance('v'), skew('s'), and/or kurtosis('k')\\n\",\n \"mean,var= binom.stats(n_A,p_A)\\n\",\n \"\\n\",\n \"print( mean)\\n\",\n \"print( var**0.5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Looks like it matches up with our manual methods. Note: we did not round in this case.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### We can also get the probability mass function:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's try another example to see the full PMF (Probability Mass Function) and plotting it.\\n\",\n \"\\n\",\n \"Imagine you flip a fair coin. Your probability of getting a heads is p=0.5 (success in this example).\\n\",\n \"\\n\",\n \"So what does your probability mass function look like for 10 coin flips?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 65,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"array([0.00097656, 0.00976563, 0.04394531, 0.1171875 , 0.20507812,\\n\",\n \" 0.24609375, 0.20507812, 0.1171875 , 0.04394531, 0.00976563,\\n\",\n \" 0.00097656])\"\n ]\n },\n \"execution_count\": 65,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Set up a new example, let's say n= 10 coin flips and p=0.5 for a fair coin.\\n\",\n \"n=10\\n\",\n \"p=0.5\\n\",\n \"\\n\",\n \"# Set up n success, remember indexing starts at 0, so use n+1\\n\",\n \"x = range(n+1)\\n\",\n \"\\n\",\n \"# Now create the probability mass function\\n\",\n \"Y = binom.pmf(x,n,p)\\n\",\n \"\\n\",\n \"#Show\\n\",\n \"Y\\n\",\n \"\\n\",\n \"# Next we'll visualize the pmf by plotting it.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Finally, let's plot the binomial distribution to get the full picture.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 77,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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L1yeTdY0qA8zwJJ35C0bq7d7ZbPSSQdXYmF1OQYwDuS9pO0e07mC0hJ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\\n\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"# For simple plots, matplotlib is fine, seaborn is unnecessary.\\n\",\n \"\\n\",\n \"# Now simply use plot\\n\",\n \"plt.plot(x,Y,'o')\\n\",\n \"\\n\",\n \"#Title (use y=1.08 to raise the long title a little more above the plot)\\n\",\n \"plt.title('Binomial Distribution PMF: 10 coin Flips, Odds of Success for Heads is p=0.5',y=1.08)\\n\",\n \"\\n\",\n \"#Axis Titles\\n\",\n \"plt.xlabel('Number of Heads')\\n\",\n \"plt.ylabel('Probability')\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"That's it for the review on Binomial Distributions. More info can be found at the following sources:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Binomial_distribution\\n\",\n \"\\n\",\n \"2.) http://stattrek.com/probability-distributions/binomial.aspx\\n\",\n \"\\n\",\n \"3.) http://mathworld.wolfram.com/BinomialDistribution.html\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Thanks!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Chi-Square-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Chi-Square\\n\",\n \"\\n\",\n \"In this Statistics Appendix Lecture, we'll go over the Chi-Square Distribution and the Chi-Square Test. \\n\",\n \"\\n\",\n \"*Note: Before viewing this lecture, see the Hypothesis Testing Notebook Lecture.*\\n\",\n \"\\n\",\n \"Let's start by introducing the general idea of observed and theoretical frequencies, then later we'll approach the idea of the Chi-Sqaure Distribution and its definition. After that we'll do a qcuik example with Scipy on using the Chi-Square Test.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Supppose that you tossed a coin 100 times. Theoretically you would expect 50 tails and 50 heads, however it is pretty unlikely you get that result exactly. Then a question arises... how far off from you expected/theoretical frequency would you have to be in order to conclude that the observed result is statistically significant and is not just due to random variations.\\n\",\n \"\\n\",\n \"We can begin to think about this question by defining an example set of possible events. We'll call them Events 1 through *k*. Each of these events has an expected (theoretical) frequency and an observed frequency. We can display this as a table:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
EventEvent 1Event 2Event 3...Event k
Observed Frequency$$o_1$$$$o_2$$$$o_3$$...$$o_k$$
Expected Frequency$$e_1$$$$e_2$$$$e_3$$...$$e_k$$
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Since we wanted to know whether observed frequencies differ significantly from the expected frequencies we'll have to define a term for a measure of discrepency.\\n\",\n \"\\n\",\n \"We'll define this measure as Chi-Square, which will be the sum of the squared difference between the observed and expected frequency divided by the expected frequency for all events. To show this more clearly, this is mathematically written as:\\n\",\n \"$$ \\\\chi ^2 = \\\\frac{(o_1 - e_1)^2}{e_1}+\\\\frac{(o_2 - e_2)^2}{e_2}+...+\\\\frac{(o_k - e_k)^2}{e_k} $$\\n\",\n \"Which is the same as:\\n\",\n \"$$\\\\chi ^2 = \\\\sum^{k}_{j=1} \\\\frac{(o_j - e_j)^2}{e_j} $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If the total frequency is N\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sum o_j = \\\\sum e_j = N $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Then we could rewrite the Chi-Square Formula to be:\\n\",\n \"$$ \\\\chi ^2 = \\\\sum \\\\frac{o_j ^2}{e_j ^2} - N$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can now see that if the Chi Square value is equal to zero, then the observed and theoretical frequencies agree exactly. While if the Chi square value is greater than zero, they do not agree.\\n\",\n \"\\n\",\n \"The sampling distribution of Chi Square is approximated very closely by the *Chi-Square distribution*\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The Chi Square Distribution\\n\",\n \"\\n\",\n \"The Chi-Square Distribution is related to the standard normal distribution. If a random variable Z, then Z2 has the Chi Square distribution with one degree of freedom. This idea is best presented graphically in a video. I've embedded a video below which goes over this an a way better than this static iPython Notebook format.\\n\",\n \"\\n\",\n \"Here is an excellent video explaining the basics of the Chi Square Distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\"text/html\": [\n \"\\n\",\n \" \\n\",\n \" \"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import YouTubeVideo\\n\",\n \"YouTubeVideo(\\\"hcDb12fsbBU\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The Chi Square Test for Goodness of Fit\\n\",\n \"\\n\",\n \"We can now use the [Chi-Square test](http://stattrek.com/chi-square-test/goodness-of-fit.aspx?Tutorial=AP) can be used to determine how well a theoretical distribution fits an observed empirical distribution. \\n\",\n \"\\n\",\n \"Scipy will basically be constructing and looking up this table for us:\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 12,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url='http://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Chi-square_distributionCDF-English.png/300px-Chi-square_distributionCDF-English.png'\\n\",\n \"\\n\",\n \"from IPython.display import Image\\n\",\n \"Image(url)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"Let's go ahead and do an example problem. Say you are at a casino and are in charge of monitoring a [craps](http://en.wikipedia.org/wiki/Craps)(a dice game where two dice are rolled). You are suspcious that a player may have switched out the casino's dice for their own. How do we use the Chi-Square test to check whether or not this player is cheating?\\n\",\n \"\\n\",\n \"You will need some observations in order to begin. You begin to keep track of this player's roll outcomes.You record the next 500 rolls taking note of the sum of the dice roll result and the number of times it occurs.\\n\",\n \"\\n\",\n \"You record the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
Sum of Dice Roll23456789101112
Number of Times Observed83248596784765734287
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we also know the espected frequency of these sums for a fair dice. That frequency distribution looks like this:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
Sum of Dice Roll23456789101112
Expected Frequency1/362/363/364/365/366/365/364/363/362/361/36
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can calculated the expected number of rolls by multiplying the expected frequency with the total sum of the rolls (500 rolls).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"500\"\n ]\n },\n \"execution_count\": 20,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# Check sum of the rolls\\n\",\n \"observed = [8,32,48,59,67,84,76,57,34,28,7]\\n\",\n \"roll_sum = sum(observed)\\n\",\n \"roll_sum\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[0.027777777777777776,\\n\",\n \" 0.05555555555555555,\\n\",\n \" 0.08333333333333333,\\n\",\n \" 0.1111111111111111,\\n\",\n \" 0.1388888888888889,\\n\",\n \" 0.16666666666666666,\\n\",\n \" 0.1388888888888889,\\n\",\n \" 0.1111111111111111,\\n\",\n \" 0.08333333333333333,\\n\",\n \" 0.05555555555555555,\\n\",\n \" 0.027777777777777776]\"\n ]\n },\n \"execution_count\": 22,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# The expected frequency\\n\",\n \"freq = [1,2,3,4,5,6,5,4,3,2,1]\\n\",\n \"\\n\",\n \"# Note use of float for python 2.7\\n\",\n \"possible_rolls = 1.0/36\\n\",\n \"\\n\",\n \"freq = [possible_rolls*dice for dice in freq]\\n\",\n \"\\n\",\n \"#Check\\n\",\n \"freq\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Excellent, now let's multiply our frequency by the sum to get the expected number of rolls for each frequency.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[13.888888888888888,\\n\",\n \" 27.777777777777775,\\n\",\n \" 41.666666666666664,\\n\",\n \" 55.55555555555555,\\n\",\n \" 69.44444444444444,\\n\",\n \" 83.33333333333333,\\n\",\n \" 69.44444444444444,\\n\",\n \" 55.55555555555555,\\n\",\n \" 41.666666666666664,\\n\",\n \" 27.777777777777775,\\n\",\n \" 13.888888888888888]\"\n ]\n },\n \"execution_count\": 25,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"expected = [roll_sum*f for f in freq]\\n\",\n \"expected\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can now use Scipy to perform the [Chi Square Test](http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.chisquare.html) by using chisquare.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The chi-squared test statistic is 9.89\\n\",\n \"The p-value for the test is 0.45\\n\"\n ]\n }\n ],\n \"source\": [\n \"from scipy import stats\\n\",\n \"\\n\",\n \"chisq,p = stats.chisquare(observed,expected)\\n\",\n \"\\n\",\n \"print( 'The chi-squared test statistic is %.2f' %chisq)\\n\",\n \"print( 'The p-value for the test is %.2f' %p)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"stats.chisquare returns two values, the chi-squared test statistic and the p-value of the test.\\n\",\n \"\\n\",\n \"With such a high p-value, we have no reason to doubt the fairness of the dice.\\n\",\n \"\\n\",\n \"That's it for the Chi-Square Distirbution and Test!\\n\",\n \"\\n\",\n \"For more information, check out these links:\\n\",\n \"\\n\",\n \"1. [Wikipedia](http://en.wikipedia.org/wiki/Chi-squared_test)\\n\",\n \"\\n\",\n \"2. [Stat trek](http://stattrek.com/chi-square-test/independence.aspx)\\n\",\n \"\\n\",\n \"3. [Khan Academy](https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/pearson-s-chi-square-test-goodness-of-fit)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Continuous Uniform Distributions-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about Continous Uniform Distributions. Note: You should look at Discrete Uniform Distributions first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we took a discrete uniform distribution to probability of any outcome was 1/n for any outcome, however for a *continous* distribution, our data can not be divided in discrete components, for example weighing an object. With perfect precision on weight, the data can take on any value between two points(e.g 5.4 grams,5.423 grams, 5.42322 grams, etc.) \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that our n possible values from the discrete uniform distribution is going towards infinity, thus the probability of any *individual* outcome for a continous distribution is 1/∞ ,technically undefined or zero if we take the limit to infinity. Thus we can only take probability measurements of ranges of values, and not just a specific point. Let's look at some definitions and examples to get a better understanding!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##### A continous random variable X with a probability density function is a continous uniform random variable when:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$f(x)=\\\\frac{1}{(b-a)}\\\\\\\\\\\\\\\\a<=x<=b$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This makes sense, since for a discrete uniform distribution the f(x)=1/n but in the continous case we don't have a specific n possibilities, we have a range from the min (a) to the max (b)!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is simply the average of the min and max:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$\\\\frac{(a+b)}{2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The variance is defined as:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sigma^2 = \\\\frac{(b-a)^2}{12}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what would an example problem look like? Let's say on average, a taxi ride in NYC takes 22 minutes. After taking some time measurements from experiments we gather that all the taxi rides are uniformly distributed between 19 and 27 minutes. What is the probability density function of a taxi ride, or f(x)?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability density function results in 0.125\\n\"\n ]\n }\n ],\n \"source\": [\n \"#Let's solve this with python\\n\",\n \"\\n\",\n \"#Lower bound time\\n\",\n \"a = 19\\n\",\n \"\\n\",\n \"#Upper bound time\\n\",\n \"b = 27\\n\",\n \"\\n\",\n \"#Then using our probability density function we get\\n\",\n \"fx = 1.0/(b-a)\\n\",\n \"\\n\",\n \"#show \\n\",\n \"print('The probability density function results in %1.3f' %fx)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The variance of the continous unifrom distribution is 5.3\\n\"\n ]\n }\n ],\n \"source\": [\n \"#We can also get the variance \\n\",\n \"var = ((b-a)**2 )/12\\n\",\n \"\\n\",\n \"#Show\\n\",\n \"print('The variance of the continous unifrom distribution is %1.1f' %var)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So let's ask the question, what's the probability that the taxi ride will last *at least* 25 minutes?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" The probability that the taxi ride will last at least 25 minutes is 25.0%\\n\"\n ]\n }\n ],\n \"source\": [\n \"# This is the same as the PDF of f(27) (the entire space) minus the probability space less than 25 minutes.\\n\",\n \"\\n\",\n \"#f(27)\\n\",\n \"fx_1 = 27.0/(b-a)\\n\",\n \"#f(25)\\n\",\n \"fx_2 = 25.0/(b-a)\\n\",\n \"\\n\",\n \"#Our answer is then\\n\",\n \"ans = fx_1-fx_2\\n\",\n \"\\n\",\n \"#print\\n\",\n \"print(' The probability that the taxi ride will last at least 25 minutes is %2.1f%%' %(100*ans))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to do this automatically with scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 37,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 37,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Import the following\\n\",\n \"from scipy.stats import uniform\\n\",\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"#Let's set an A and B\\n\",\n \"A=0\\n\",\n \"B=5\\n\",\n \"\\n\",\n \"# Set x as 100 linearly spaced points between A and B\\n\",\n \"x = np.linspace(A,B,100)\\n\",\n \"\\n\",\n \"# Use uniform(loc=start point,scale=endpoint)\\n\",\n \"rv = uniform(loc=A,scale=B)\\n\",\n \"\\n\",\n \"#Plot the PDF of that uniform distirbution\\n\",\n \"plt.plot(x,rv.pdf(x))\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Note the above line is at 0.2, as we would expect since 1/(5-0) is 1/5 or 0.2.\\n\",\n \"\\n\",\n \"####That's it for Uniform Continuous Distributions. Here are some more resource for you:\\n\",\n \"\\n\",\n \"1.)http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29\\n\",\n \"\\n\",\n \"2.)http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html\\n\",\n \"\\n\",\n \"3.)http://mathworld.wolfram.com/UniformDistribution.html\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Discrete Uniform Distributions-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Let's start off with a definition for discrete uniform distributions.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Definition: A random variable X has a discrete uniform distribution if each of the n values in its range:\\n\",\n \" x1,x2,x3....xn has equal probability:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ f(x_{i}) = 1/n $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's use python to show a simple example!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First the imports:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Import all the usual imports from the Python for Data Analysis and Visualization Course.\\n\",\n \"import numpy as np\\n\",\n \"from numpy.random import randn\\n\",\n \"import pandas as pd\\n\",\n \"from scipy import stats\\n\",\n \"import matplotlib as mpl\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"from __future__ import division\\n\",\n \"%matplotlib inline\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's set up a dice roll and plot the distribution using seaborn before we go use matplotlib by itself.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Probability Mass Function for Dice Roll')\"\n ]\n },\n \"execution_count\": 8,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# How about a roll of a dice?\\n\",\n \"\\n\",\n \"# Let's check out the Probability Mass function!\\n\",\n \"\\n\",\n \"# Each number\\n\",\n \"roll_options = [1,2,3,4,5,6]\\n\",\n \"\\n\",\n \"# Total probability space\\n\",\n \"tprob = 1\\n\",\n \"\\n\",\n \"# Each roll has same odds of appearing (on a fair die at least)\\n\",\n \"prob_roll = tprob / len(roll_options)\\n\",\n \"\\n\",\n \"# Plot using seaborn rugplot (note this is not really a rugplot), setting height equal to probability of roll\\n\",\n \"uni_plot = sns.rugplot(roll_options,height=prob_roll,c='indianred')\\n\",\n \"\\n\",\n \"# Set Title\\n\",\n \"uni_plot.set_title('Probability Mass Function for Dice Roll')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can see in the above example that the f(x) value on the plot is just equal to 1/(Total Possible Outcomes)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"-------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what's the mean and variance of this uniform distribution? \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is simply the max and min value divided by two, just like the mean of two numbers.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\mu = (b+a)/2 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"With a variance of:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sigma^2=\\\\frac{(b-a+1)^2 - 1 }{12}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"--------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to automatically create a Discrete Uniform Distribution using Scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The mean is 3.5\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Imports\\n\",\n \"from scipy.stats import randint\\n\",\n \"\\n\",\n \"#Set up a low and high boundary for dice roll ( go to 7 since index starts at 0)\\n\",\n \"low,high = 1,7\\n\",\n \"\\n\",\n \"# Get mean and variance\\n\",\n \"mean,var = randint.stats(low,high)\\n\",\n \"\\n\",\n \"print('The mean is %2.1f' % mean)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 26,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Now we can make a simple bar plot\\n\",\n \"plt.bar(roll_options,randint.pmf(roll_options,low,high))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#####That's basically it for a discrete uniform distribution, check out the rest of the reading below if you're still interested.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"---------------------------------------------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Example of real world use: German Tank Problem\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now that we know some information about the uniform discrete distribution function, how about we use it to solve a problem?\\n\",\n \"\\n\",\n \"In this case we'll solve the famous German Tank Problem.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For background, first read the wikipedia page: http://en.wikipedia.org/wiki/German_tank_problem\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Excerpt from Wikipedia:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\\"In the statistical theory of estimation, the problem of estimating the maximum of a discrete uniform distribution from sampling without replacement is known in English as the German tank problem, due to its application in World War II to the estimation of the number of German tanks. Estimating the population maximum based on a single sample yields divergent results, while the estimation based on multiple samples is an instructive practical estimation question whose answer is simple but not obvious.\\\"\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"After reading the Wikipedia article, check out the following code for an example Python workout of the example problem.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Using a Minimum-variance unbiased estimator we obtain the population max is equal to :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ Population\\\\max = sample \\\\max + \\\\frac{sample \\\\max}{sample \\\\ size} -1 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we for instance captured 5 tanks with the serial numbers 3,7,11,16 then we know the max observed serial number was m=16.\\n\",\n \"This is our sample max with a sample size of 5 tanks. Plugging into the MVUE results in:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 38,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"18.2\"\n ]\n },\n \"execution_count\": 38,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"tank_estimate = 16 + (16/5) - 1\\n\",\n \"tank_estimate\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For a Bayseian Approach:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 41,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"20.0\"\n ]\n },\n \"execution_count\": 41,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"m=16\\n\",\n \"k=5\\n\",\n \"tank_b_estimate = (m-1)*( (k-1)/ ( k-2) )\\n\",\n \"tank_b_estimate\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Remember, this is still missing the STD\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Exponential Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Frequentist A-B Testing-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Gamma Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Hypothesis Testing and Confidence Intervals-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Hypothesis Testing\\n\",\n \"\\n\",\n \"Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. \\n\",\n \"\\n\",\n \"Hypothesis Testing can be broken into 10 basic steps.\\n\",\n \"\\n\",\n \" 1.) Data Testing\\n\",\n \" 2.) Assumptions\\n\",\n \" 3.) Hypothesis\\n\",\n \" 4.) Test Statistic\\n\",\n \" 5.) Distribution of Test Statistic\\n\",\n \" 6.) Decision Rule\\n\",\n \" 7.) Calculation of Test Statistic\\n\",\n \" 8.) Statistical Decision\\n\",\n \" 9.) Conclusion\\n\",\n \" 10.) p-values\\n\",\n \" \\n\",\n \"It is important to note that the initial steps can be done in different orders or at the same time, specifically, I would suggest you come up with you research question first, before going out to do data testing. Moving along:\\n\",\n \"\\n\",\n \"Let's now break down these steps:\\n\",\n \"\\n\",\n \"##### Step 1: Data Testing\\n\",\n \"\\n\",\n \"This one is pretty simple, to do any sort of statistical testing, we'll need some data from a population.\\n\",\n \"\\n\",\n \"##### Step 2: Assumptions\\n\",\n \"\\n\",\n \"We will need to make some assumptions regarding our data, such as assuming the data is normally distributed, or what the Standard Deviation of the data is. Another example would be whether to use a T-Distribution or a Normal Distribution.\\n\",\n \"\\n\",\n \"##### Step 3: Hypothesis\\n\",\n \"\\n\",\n \"In our Hypothesis Testing, we will have two Hypothesis: *The Null Hypothesis* (denoted as Ho) and the *Alternative Hypothesis* (denoted as HA). The Null Hypothesis is the hypothesis we are looking to test against the alternative hypothesis. Let's get an example of what this looks like:\\n\",\n \"\\n\",\n \"Let's assume we have a data set regarding ages of customers to a restaurant. Let's say for this particular data set we want to try to prove that the mean of that sample population is *not* 30. So we set our null hypothesis as:\\n\",\n \"\\n\",\n \"$$ H_o : \\\\mu = 30 $$\\n\",\n \"And our Alternative Hypothesis as:\\n\",\n \"$$ H_A : \\\\mu \\\\neq 30 $$ \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We could have also set out Alternative Hypothesis to be that the mean is greater than 30 or another Alternative Hypothesis we could have proposed is the mean is less than 30. We will discuss these other options later when we go into one-tail versus two-tail tests.\\n\",\n \"\\n\",\n \"Continuing on with our steps:\\n\",\n \"\\n\",\n \"##### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"Based on our assumptions, we'll choose a suitable test statistic. For example, if we believe to have a normal distribution with our data we would choose a z-score as our standard error:\\n\",\n \"\\n\",\n \"$$ z = \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}}$$\\n\",\n \"\\n\",\n \"Or if we assume to have a t-distribution we would choose a t-score (estimated standard error):\\n\",\n \"\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"\\n\",\n \"Then our test statistic is defined as:\\n\",\n \"\\n\",\n \"$$ Test \\\\ Statistic = \\\\frac{Relevant \\\\ Statistic - Hypothesized \\\\ Parameter}{ Standard \\\\ Error \\\\ of \\\\ Releveant \\\\ Statistic}$$\\n\",\n \"\\n\",\n \"\\n\",\n \"##### Step 5: Distribution of Test Statistic\\n\",\n \"\\n\",\n \"As discussed earlier, verify that whether your data should use a t or z distribution.\\n\",\n \"\\n\",\n \"##### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"Considering the distribution, we need to establish a significance level, usually denoted as alpha, α. Alpha is the probability of having a Null Hypothesis that is true, but our data shows is wrong. So alpha is the probability of rejecting a *true* Null Hypothesis. By convention, alpha is usually equal to 0.05 or 5%. This means that 5% of the time, we will falsely reject a true null hypothesis, this is best explained through a picture.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 11,\n \"metadata\": {\n \"image/jpeg\": {\n \"height\": 400,\n \"width\": 600\n }\n },\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import Image\\n\",\n \"url = 'http://images.flatworldknowledge.com/shafer/shafer-fig08_004.jpg'\\n\",\n \"Image(url,height=400,width=600)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The above image shows three types of tests. It shows 2 types of One-Tail Tests on top, and a Two-Tail Test on the bottom. You apply your significance level to a region depending on your Alternative Hypothesis (shown above each distribution).\\n\",\n \"\\n\",\n \"Let's look at the bottom two-tail test. With an alpha=0.05, then whenever we take a sample and get our test statistic (the t or z score) then we check where it falls in our distribution. If the Null Hypothesis is True, then 95% of the time it would land inbetween the α/2 markers. So if our test statistic lands inbetween the alpha markers (for a two tail test inbetween α/2, for a one tail test either below or above the α marker depending on the Alternative Hypothesis) we accept (or don't reject) the Null Hypothesis. If it landsoutside of this zone, we reject the Hypothesis.\\n\",\n \"\\n\",\n \"Now let's say we actually made a mistake, and rejected a Null Hypothesis that unknown to us was True, then we made what is called a Type I error. If we accepted a Null Hypothesis that was actually False, we've made a Type II error. Below is a handy chart depicting the error types.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 16,\n \"metadata\": {\n \"image/jpeg\": {\n \"height\": 200,\n \"width\": 300\n }\n },\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# url='http://www.personal.ceu.hu/students/08/Olga_Etchevskaia/images/errors.jpg'\\n\",\n \"url='https://dfrieds.com/images/errors.jpg'\\n\",\n \"Image(url,height=200,width=300)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##### Step 7: Calculate the Test Statistic\\n\",\n \"Now that we understand our decision rule we can calculate our t or z score.\\n\",\n \"\\n\",\n \"##### Step 8: Statistical Decision\\n\",\n \"\\n\",\n \"We take what we understand from Step 6 and see where our test statistic from Step 7 lies.\\n\",\n \"\\n\",\n \"##### Step 9: Conclusion\\n\",\n \"\\n\",\n \"We check our statistical decision and conclude whether or not to reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"##### Step 10: Calculate a p-value\\n\",\n \"\\n\",\n \"The [P value](http://en.wikipedia.org/wiki/P-value) is the estimated probability of rejecting the null hypothesis of a study question when that null hypothesis is actually true. In other words, the P-value may be considered the probability of finding the observed, or more extreme, results when the null hypothesis is true – the definition of ‘extreme’ depends on how the hypothesis is being tested.\\n\",\n \"\\n\",\n \"It is very important to note: Since the p-value is used in Frequentist inference (and not Bayesian inference), it does not in itself support reasoning about the probabilities of hypotheses, but only as a tool for deciding whether to reject the null hypothesis in favor of the alternative hypothesis.\\n\",\n \"\\n\",\n \"Let's now go over an example to go through all the steps!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Example Problem 1\\n\",\n \"\\n\",\n \"There are two main types of single-sample hypothesis tests:\\n\",\n \"\\n\",\n \" 1.) When the population standard deviation σ is known or given.\\n\",\n \" 2.) When the population standard deviation σ is NOT known, and therefore we have to estimate \\n\",\n \" with s, the sample standard deviation.\\n\",\n \"\\n\",\n \"For Case 1, we use a normal (Z) distribution, for Case 2, we use the T-distribution.\\n\",\n \"\\n\",\n \"Let's start with an example. We are hired by a fast food chain to figure out the mean age of customers. The current CEO believes the mean age is 30, however we don't believe that to be True. So we now have our Null and Alternative Hypotheses:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"It is important to remember that the Null and Alternative Hypotheses must account for all possible outcomes. \\n\",\n \"\\n\",\n \"So now we will see if we can reject the Null Hypothesis in order to accept our Alternative Hypothesis. \\n\",\n \"\\n\",\n \"#### Step 1: Data\\n\",\n \"\\n\",\n \"So we take a random sample of customers and come up with the following data. From our *sample population*, we get a mean age of 27 years from a sample of 10 customers. Note: This is a sample population of the total population (referred to as just the population).\\n\",\n \"\\n\",\n \"#### Step 2: Assumptions\\n\",\n \"We will begin and get some assumptions. Based on some textbook sources you check, you assume that the population follows a normal distribution (Note: There are [specific tests](http://en.wikipedia.org/wiki/Normality_test) to check this). We also see in this textbook that given the population we could assume a variance of 20, so a standard deviation of:\\n\",\n \"\\n\",\n \"$$ \\\\sigma = \\\\sqrt{20}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"It's important to note that in a real world case it is unlikely to know the population variance, and we will discuss that in the next example. Usually you will only know your sample population's standard deviation (not the *entire* population's standard deviation).Given that we know the standard deviation, we can use a Z Distribution.\\n\",\n \"\\n\",\n \"#### Step 3: Hypothesis\\n\",\n \"\\n\",\n \"We already have our Hypotheses from above:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\\n\",\n \"\\n\",\n \"#### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"Since we have the standard deviation, we can use the Z-Statistic:\\n\",\n \"$$ z = \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}}$$\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Step 5: Distribution\\n\",\n \"\\n\",\n \"Again we have chosen the Z-Distribution, having a mean and max at zero.\\n\",\n \"\\n\",\n \"#### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"We will set our significance level (alpha) at 5%. Meaning we are trying to minimize our Type I error. So we are trying to make sure we can reject the Null Hyopthesis and minimize the chance that it was actually True. By choosing 5% we will have a certainty of 95% that we are correct if we reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 7: Calculation of Test Statistic\\n\",\n \"\\n\",\n \"Let's go ahead and calculate our Test Statistic:\\n\",\n \"$$ z= \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}} = \\\\frac{27 - 30}{\\\\sqrt{20} / \\\\sqrt{10}} = -2.12 $$\\n\",\n \"\\n\",\n \"#### Step 8: Conclusion\\n\",\n \"\\n\",\n \"In order to accept or reject the Null Hypothesis we need to see where our Z score lands. If we take alpha to be 95% then we know from a [Z-Score Table](http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf) that we have to lie above 1.96 or below -1.96 as seen in the figure below:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/gif\": \"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\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 27,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url='https://www.sfu.ca/personal/archives/richards/Zen/Media/Ch17-9.gif'\\n\",\n \"Image(url)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Given that our Z-score for our Test Statistic was -2.12, we can see that we can reject the Null Hypothesis! So we reject that the mean of the customer age is 30. Remember, this test does not actually tell us what the mean is, only that it unlikely to be 30. How unlikely? This is where the p-value comes into play.\\n\",\n \"\\n\",\n \"#### Step 9: p-value\\n\",\n \"\\n\",\n \"From a table, we can see that 98.3% corresponds to the percentage of the area inbetween our +/- of our Z-Score, 2.12. This means that if the reality is the Null Hypothesis is actually True, we would only find that data 100-98.3= 1.7% of the time. So our p-value is 1.7% (or 0.017). This is pretty unlikely so we can be quite confident in our rejection of the Null Hypothesis.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Confidence Intervals\\n\",\n \"\\n\",\n \"We could describe the above process using confidence intervals. The equation for a confidence interval is:\\n\",\n \"$$ \\\\bar{x} \\\\pm z \\\\sigma _\\\\bar{x} $$\\n\",\n \"\\n\",\n \"From our work above we can fill in the equation as:\\n\",\n \"$$ 27 \\\\pm 1.96 *(\\\\frac{\\\\sqrt{20}}{\\\\sqrt{10}}) $$\\n\",\n \"\\n\",\n \"Which (with rounding) is equal to:\\n\",\n \"$$ 27 \\\\pm 2.77 $$\\n\",\n \"\\n\",\n \"This gives us a range between 24.23 and 29.77. Since the Null Hypothesis mean of 30 is NOT in that range, we can reject that Null Hypothesis. A simple approach to the above problem!\\n\",\n \"\\n\",\n \"Now what is we don't know the standard deviation? Let's go ahead and look at an example problem:\\n\",\n \"\\n\",\n \"### Example Problem 2\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Assuming the same problem as before, we want to know whether or not we can reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 1: Data\\n\",\n \"\\n\",\n \"Let's say after getting our data, we have a mean of 27 form 10 customers. Our *sample population* has a standard deviation of 3.\\n\",\n \"\\n\",\n \"#### Step 2: Assumptions\\n\",\n \"\\n\",\n \"In this second case we don't consult a textbook so we don't know what the entire populations standard deviation is.\\n\",\n \"\\n\",\n \"\\n\",\n \"#### Step 3: Hypotheses\\n\",\n \"\\n\",\n \"Same as before:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\\n\",\n \"\\n\",\n \"#### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"We now have to use the t-distribution since we don't know the populations standard deviation. So our test statistic will be:\\n\",\n \"\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"#### Step 5: Distribution\\n\",\n \"\\n\",\n \"Since we only have 10 customers in our sample and don't know the entire population's standard deviation we use a t-distribution. Remember as a sample population grows beyond 30, the t distribution begins to resemble and behave like a standard Z distribution. Keep in mind a t-distribution is \\\"flatter\\\" and operates on degrees of freedom (n-1).\\n\",\n \"\\n\",\n \"We can use a [T-table](http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf) to find that for a 95% significance level, our region for accepting the Null Hypothesis falss between +/- 2.262\\n\",\n \"\\n\",\n \"#### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"As before: We will set our significance level (alpha) at 5%. Meaning we are trying to minimize our Type I error. So we are trying to make sure we can reject the Null Hyopthesis and minimize the chance that it was actually True. By choosing 5% we will have a certainty of 95% that we are correct if we reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 7: Calculate our Test Statistic\\n\",\n \"\\n\",\n \"Plugging into:\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"we get:\\n\",\n \"$$ t = \\\\frac{27-30}{3/ \\\\sqrt{10}}=-3.16$$\\n\",\n \"\\n\",\n \"#### Step 8: Statisitcal Decision\\n\",\n \"\\n\",\n \"Given the rejection regions was t = +/- 2.262 , then our t=-3.16 allows us to reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 9: Conclusion\\n\",\n \"\\n\",\n \"Just as before we can reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"\\n\",\n \"### Additional Resources\\n\",\n \"\\n\",\n \"Here are some more great resources for learning about Hypothesis Testing:\\n\",\n \"\\n\",\n \"1.) [Wolfram](http://mathworld.wolfram.com/HypothesisTesting.html)\\n\",\n \"2.) [Stat Trek](http://stattrek.com/hypothesis-test/hypothesis-testing.aspx)\\n\",\n \"3.) [Wikipedia](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing)\\n\",\n \"4.) [Probability Book Sample](http://www.sagepub.com/upm-data/40007_Chapter8.pdf)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Kolmogorov-Smirnov Test-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Markov Chain Monte Carlo Algorithm-checkpoint.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Normal Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"#### Let's learn the normal distribution! Note: You should check out the binomial distribution first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We'll start with the definition of the PDF, we'll see how to create the distribution in python using scipy and numpy, and discuss some properties of the normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The distribution is defined by the probability density function equation:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## $$ f(x,\\\\mu,\\\\sigma) = \\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}e^\\\\frac{-1}{2z^2} $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where: $$z=\\\\frac{(X-\\\\mu)}{\\\\sigma}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"where: μ=mean , σ=standard deviation , π=3.14... , e=2.718... The total area bounded by curve of the probability density function equation and the X axis is 1; thus the area under the curve between two ordinates X=a and X=b, where a\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import Image\\n\",\n \"Image(url='http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/The_Normal_Distribution.svg/725px-The_Normal_Distribution.svg.png')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's learn how to use scipy to create a normal distribution\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 21,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Import\\n\",\n \"import matplotlib as mpl\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Import the stats library\\n\",\n \"from scipy import stats\\n\",\n \"\\n\",\n \"# Set the mean\\n\",\n \"mean = 0\\n\",\n \"\\n\",\n \"#Set the standard deviation\\n\",\n \"std = 1\\n\",\n \"\\n\",\n \"\\n\",\n \"# Create a range\\n\",\n \"X = np.arange(-4,4,0.01)\\n\",\n \"\\n\",\n \"#Create the normal distribution for the range\\n\",\n \"Y = stats.norm.pdf(X,mean,std)\\n\",\n \"\\n\",\n \"#\\n\",\n \"plt.plot(X,Y)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's learn how to use numpy to create the normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [],\n \"source\": [\n \"#Set the mean and the standard deviaiton\\n\",\n \"mu,sigma = 0,0.1\\n\",\n \"\\n\",\n \"# Now grab 1000 random numbers from the normal distribution\\n\",\n \"norm_set = np.random.normal(mu,sigma,1000)\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n },\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"(array([ 1., 1., 0., 0., 0., 1., 1., 2., 4., 4., 7., 6., 7.,\\n\",\n \" 5., 12., 12., 25., 32., 29., 40., 34., 42., 52., 42., 47., 58.,\\n\",\n \" 72., 52., 55., 39., 42., 49., 32., 36., 27., 20., 26., 18., 19.,\\n\",\n \" 13., 15., 6., 5., 2., 3., 1., 1., 1., 0., 2.]),\\n\",\n \" array([-0.356904 , -0.34361366, -0.33032332, -0.31703298, -0.30374264,\\n\",\n \" -0.29045229, -0.27716195, -0.26387161, -0.25058127, -0.23729092,\\n\",\n \" -0.22400058, -0.21071024, -0.1974199 , -0.18412956, -0.17083921,\\n\",\n \" -0.15754887, -0.14425853, -0.13096819, -0.11767784, -0.1043875 ,\\n\",\n \" -0.09109716, -0.07780682, -0.06451648, -0.05122613, -0.03793579,\\n\",\n \" -0.02464545, -0.01135511, 0.00193524, 0.01522558, 0.02851592,\\n\",\n \" 0.04180626, 0.05509661, 0.06838695, 0.08167729, 0.09496763,\\n\",\n \" 0.10825797, 0.12154832, 0.13483866, 0.148129 , 0.16141934,\\n\",\n \" 0.17470969, 0.18800003, 0.20129037, 0.21458071, 0.22787105,\\n\",\n \" 0.2411614 , 0.25445174, 0.26774208, 0.28103242, 0.29432277,\\n\",\n \" 0.30761311]),\\n\",\n \" )\"\n ]\n },\n \"execution_count\": 30,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Now let's plot it using seaborn\\n\",\n \"\\n\",\n \"import seaborn as sns\\n\",\n \"\\n\",\n \"plt.hist(norm_set,bins=50)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"There's a ton on information to go over for the normal distribution, this notebook should just serve as a very mild introduction, for more info check out the following sources:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Normal_distribution\\n\",\n \"\\n\",\n \"2.) http://mathworld.wolfram.com/NormalDistribution.html\\n\",\n \"\\n\",\n \"3.) http://stattrek.com/probability-distributions/normal.aspx\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Thanks!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Poisson Distribution-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about the Poisson Distribution! \\n\",\n \"Note: I suggest you learn about the binomial distribution first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"A poisson distribution focuses on the number of discrete events or occurrences over a specified interval or continuum (e.g. time,length,distance,etc.). We'll look at the formal definition, get a break down of what that actually means, see an example and then look at the other characteristics such as mean and standard deviation.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Formal Definition: A discrete random variable X has a Poisson distribution with parameter λ if for k=0,1,2.., the probability mass function of X is given by:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$Pr(X=k)=\\\\frac{\\\\lambda^ke^{-\\\\lambda}}{k!}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"where e is Euler's number (e=2.718...) and k! is the factorial of k.\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The Poisson Distribution has the following characteristics:\\n\",\n \"\\n\",\n \" 1.) Discrete outcomes (x=0,1,2,3...)\\n\",\n \" 2.) The number of occurrences can range from zero to infinity (theoretically). \\n\",\n \" 3.) It describes the distribution of infrequent (rare) events.\\n\",\n \" 4.) Each event is independent of the other events.\\n\",\n \" 5.) Describes discrete events over an interval such as a time or distance.\\n\",\n \" 6.) The expected number of occurrences E(X) are assumed to be constant throughout the experiment.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what would an example question look like? \\n\",\n \"\\n\",\n \"Let's say a McDonald's has a lunch rush from 12:30pm to 1:00pm. From looking at customer sales from previous days, we know that on average 10 customers enter during 12:30pm to 1:00pm. What is the probability that *exactly* 7 customers enter during lunch rush? What is the probability that *more than* 10 customers arrive? \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's begin by thinking about how many customers we expect to come into McDonald's during lunch rush. Well we were actually already given that information, it's 10. This means that the mean is 10, then our expected value E(X)=10. In the Poisson distribution this is λ. So the mean = λ for a Poisson Distribution, it is the expected number of occurences over the specfied interval.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So since we now know what λ is, we can plug the information into the probability mass function and get an answer, let's use python and see how this works. Let's start off by answering the first question: \\n\",\n \"\\n\",\n \"What is the probability that exactly 7 customers enter during lunch rush?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 45,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" There is a 9.01 % chance that exactly 7 customers show up at the lunch rush\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Note do not use lambda as an object name in python! It is already used for special lambda functions in Python!!\\n\",\n \"\\n\",\n \"# Set lambda\\n\",\n \"lamb = 10\\n\",\n \"\\n\",\n \"# Set k to the number of occurences\\n\",\n \"k=7\\n\",\n \"\\n\",\n \"#Set up e and factorial math statements\\n\",\n \"from math import exp\\n\",\n \"from math import factorial\\n\",\n \"from __future__ import division\\n\",\n \"\\n\",\n \"# Now put the probability mass function\\n\",\n \"prob = (lamb**k)*exp(-lamb)/factorial(k)\\n\",\n \"\\n\",\n \"# Put into percentage form and print answer\\n\",\n \"print( ' There is a %2.2f %% chance that exactly 7 customers show up at the lunch rush' %(100*prob))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we've seen how to create the PMF manually, let's see how to do it automatically with scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"There is a 9.01 % chance that exactly 7 customers show up at the lunch rush\\n\",\n \"The mean is 10.00 \\n\"\n ]\n }\n ],\n \"source\": [\n \"# Import the dsitrubtion from scipy.stats\\n\",\n \"from scipy.stats import poisson\\n\",\n \"\\n\",\n \"# Set our mean = 10 customers for the lunch rush\\n\",\n \"mu = 10\\n\",\n \"\\n\",\n \"# Then we can get the mean and variance\\n\",\n \"mean,var = poisson.stats(mu)\\n\",\n \"\\n\",\n \"# We can also calculate the PMF at specific points, such as the odds of exactly 7 customers\\n\",\n \"odds_seven = poisson.pmf(7,mu)\\n\",\n \"\\n\",\n \"#Print\\n\",\n \"print( 'There is a %2.2f %% chance that exactly 7 customers show up at the lunch rush' %(100*odds_seven))\\n\",\n \"\\n\",\n \"# Print the mean\\n\",\n \"print( 'The mean is %2.2f ' %mean)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Awesome! Our manual results match up with scipy's built in stats distribution generator!\\n\",\n \"\\n\",\n \"Now what if we wanted to see the entire distribution? We'll need this information to answer the second question.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# Now let's get the PMF and plot it\\n\",\n \"\\n\",\n \"# First the PMF\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Let's see the PMF for all the way to 30 customers, remeber theoretically an infinite number of customers could show up.\\n\",\n \"k=np.arange(30)\\n\",\n \"\\n\",\n \"# Average of 10 customers for the time interval\\n\",\n \"lamb = 10\\n\",\n \"\\n\",\n \"#The PMF we'll use to plot\\n\",\n \"pmf_pois = poisson.pmf(k,lamb)\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 24,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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NofXt7uxYsWKDMzEy1tbVpxYoVWr58uXbs2OGrGRwc1Lx589TR0aEXXnhB7733njZt2qRp06aFfmYAAGDcsP0poYqKCi1btky5ubmSpMrKSu3Zs0fV1dUqLy8PqK+pqdH06dNVWVkpSUpJSVFLS4vWrVunxYsXS5I2b96sTz75RE1NTYqMjJQkJSYmhnpOAABgnLG1wjI4OKjW1la53W6/cbfbraampqD7NDc3B9TPnz9fLS0tOnnypCTppZdeUnp6uh588EHFxsYqNTVVjz/+uIaGhs7ay8DAgPr7+/02AAAwPtkKLL29vRoaGlJsbKzfeGxsrLxeb9B9vF5v0PpTp06pt7dXkvThhx/qhRde0NDQkOrr67Vy5Uo99dRTWrNmzVl7KS8vV3R0tG9LSEiwcyoAAGAMCelNt2FhYX6PLcsKGDtf/RfHh4eHddVVV2njxo1yuVy66667VFpaqurq6rMes6SkRMeOHfNtXV1doZwKAAAYA2y9hyUmJkbh4eEBqyk9PT0BqyhnxMXFBa2PiIjQ5MmTJUlTp05VZGSkwsPDfTUpKSnyer0aHBxUVFRUwHEdDoccDoed9gEAwBhla4UlKipKLpdLHo/Hb9zj8SgjIyPoPunp6QH1DQ0NSktL873B9gc/+IH+/e9/a3h42Ffz/vvva+rUqUHDCgAAuLTYviVUVFSkZ599Vps3b9bhw4dVWFiozs5O5eXlSTp9q2bp0qW++ry8PB05ckRFRUU6fPiwNm/erNraWj3yyCO+mgceeEB9fX16+OGH9f7772v37t16/PHH9eCDD16EUwQAAGOd7Y81Z2dnq6+vT6tXr1Z3d7dSU1NVX1/v+xhyd3e333eyJCcnq76+XoWFhdqwYYPi4+O1fv1630eaJSkhIUENDQ0qLCzUDTfcoGnTpunhhx/W7373u4twigAAYKwL6dea8/PzlZ+fH/S5LVu2BIzNmTNHBw4cOOcx09PT9eabb4bSDgAAGOf4LSEAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeBGj3QCAS0tS8W5b9R1rF45QJwDGElZYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYL6TAUlVVpeTkZDmdTrlcLu3fv/+c9Y2NjXK5XHI6nZoxY4ZqamrOWrt9+3aFhYXpzjvvDKU1AAAwDtkOLHV1dSooKFBpaana2tqUmZmprKwsdXZ2Bq1vb2/XggULlJmZqba2Nq1YsULLly/Xjh07AmqPHDmiRx55RJmZmfbPBAAAjFu2A0tFRYWWLVum3NxcpaSkqLKyUgkJCaqurg5aX1NTo+nTp6uyslIpKSnKzc3Vfffdp3Xr1vnVDQ0N6Re/+IUee+wxzZgxI7SzAQAA45KtwDI4OKjW1la53W6/cbfbraampqD7NDc3B9TPnz9fLS0tOnnypG9s9erVmjJlipYtW3ZBvQwMDKi/v99vAwAA45OtwNLb26uhoSHFxsb6jcfGxsrr9Qbdx+v1Bq0/deqUent7JUlvvPGGamtrtWnTpgvupby8XNHR0b4tISHBzqkAAIAxJKQ33YaFhfk9tiwrYOx89WfGjx8/rl/+8pfatGmTYmJiLriHkpISHTt2zLd1dXXZOAMAADCWRNgpjomJUXh4eMBqSk9PT8AqyhlxcXFB6yMiIjR58mS9++676ujo0O233+57fnh4+HRzERF67733dM011wQc1+FwyOFw2GkfAACMUbZWWKKiouRyueTxePzGPR6PMjIygu6Tnp4eUN/Q0KC0tDRFRkZq5syZOnTokA4ePOjb7rjjDv3oRz/SwYMHudUDAADsrbBIUlFRkXJycpSWlqb09HRt3LhRnZ2dysvLk3T6Vs3Ro0e1detWSVJeXp6eeeYZFRUV6f7771dzc7Nqa2v1/PPPS5KcTqdSU1P9XuPrX/+6JAWMAwCAS5PtwJKdna2+vj6tXr1a3d3dSk1NVX19vRITEyVJ3d3dft/JkpycrPr6ehUWFmrDhg2Kj4/X+vXrtXjx4ot3FgAAYFyzHVgkKT8/X/n5+UGf27JlS8DYnDlzdODAgQs+frBjYOxIKt5tq75j7cIR6gQAMF7wW0IAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPFC+uI4ABgNfCkhcOlihQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxosY7QYA4H8hqXi3rfqOtQtHqBMAoQhphaWqqkrJyclyOp1yuVzav3//OesbGxvlcrnkdDo1Y8YM1dTU+D2/adMmZWZmatKkSZo0aZLmzp2rt99+O5TWAADAOGQ7sNTV1amgoEClpaVqa2tTZmamsrKy1NnZGbS+vb1dCxYsUGZmptra2rRixQotX75cO3bs8NXs27dPd999t/bu3avm5mZNnz5dbrdbR48eDf3MAADAuGE7sFRUVGjZsmXKzc1VSkqKKisrlZCQoOrq6qD1NTU1mj59uiorK5WSkqLc3Fzdd999Wrduna9m27Ztys/P14033qiZM2dq06ZNGh4e1iuvvBL6mQEAgHHDVmAZHBxUa2ur3G6337jb7VZTU1PQfZqbmwPq58+fr5aWFp08eTLoPidOnNDJkyd15ZVXnrWXgYEB9ff3+20AAGB8shVYent7NTQ0pNjYWL/x2NhYeb3eoPt4vd6g9adOnVJvb2/QfYqLizVt2jTNnTv3rL2Ul5crOjratyUkJNg5FQAAMIaE9KbbsLAwv8eWZQWMna8+2LgkPfHEE3r++ee1c+dOOZ3Osx6zpKREx44d821dXV12TgEAAIwhtj7WHBMTo/Dw8IDVlJ6enoBVlDPi4uKC1kdERGjy5Ml+4+vWrdPjjz+ul19+WTfccMM5e3E4HHI4HHbaBwAAY5StwBIVFSWXyyWPx6Of/vSnvnGPx6NFixYF3Sc9PV1/+ctf/MYaGhqUlpamyMhI39iTTz6p//u//9OePXuUlpZmpy2MAL6zAgBgEtu3hIqKivTss89q8+bNOnz4sAoLC9XZ2am8vDxJp2/VLF261Fefl5enI0eOqKioSIcPH9bmzZtVW1urRx55xFfzxBNPaOXKldq8ebOSkpLk9Xrl9Xr16aefXoRTBAAAY53tb7rNzs5WX1+fVq9ere7ubqWmpqq+vl6JiYmSpO7ubr/vZElOTlZ9fb0KCwu1YcMGxcfHa/369Vq8eLGvpqqqSoODg1qyZInfa5WVlenRRx8N8dQAAMB4EdJX8+fn5ys/Pz/oc1u2bAkYmzNnjg4cOHDW43V0dITSBgAAuETw44cAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjBfSrzUDwKUkqXi37X061i4cgU6ASxcrLAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGixjtBjBykop326rvWLtwhDoBAOCrIbAAwAjjfx6Ar45bQgAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeHzTLQAYjG/JBU5jhQUAABiPwAIAAIxHYAEAAMbjPSyG4/41AAAEFgAYt/gfHownId0SqqqqUnJyspxOp1wul/bv33/O+sbGRrlcLjmdTs2YMUM1NTUBNTt27NCsWbPkcDg0a9Ys7dq1K5TWAADAOGQ7sNTV1amgoEClpaVqa2tTZmamsrKy1NnZGbS+vb1dCxYsUGZmptra2rRixQotX75cO3bs8NU0NzcrOztbOTk5euedd5STk6Of//zneuutt0I/MwAAMG7YviVUUVGhZcuWKTc3V5JUWVmpPXv2qLq6WuXl5QH1NTU1mj59uiorKyVJKSkpamlp0bp167R48WLfMebNm6eSkhJJUklJiRobG1VZWannn38+1HMDAISI20kwja3AMjg4qNbWVhUXF/uNu91uNTU1Bd2nublZbrfbb2z+/Pmqra3VyZMnFRkZqebmZhUWFgbUnAk5wQwMDGhgYMD3+NixY5Kk/v5+O6c04lLL9tje5/89Nt/35+GBE7b2/eL5s6+Z+47ma7Pv/2bf0XxtE/a1+/feF//Ow6XnzNyxLOvchZYNR48etSRZb7zxht/4mjVrrGuvvTboPt/85jetNWvW+I298cYbliTro48+sizLsiIjI61t27b51Wzbts2Kioo6ay9lZWWWJDY2NjY2NrZxsHV1dZ0zg4T0KaGwsDC/x5ZlBYydr/7L43aPWVJSoqKiIt/j4eFhffLJJ5o8efI597tY+vv7lZCQoK6uLk2cOHHEX2+s43rZw/W6cFwre7he9nC9Llyo18qyLB0/flzx8fHnrLMVWGJiYhQeHi6v1+s33tPTo9jY2KD7xMXFBa2PiIjQ5MmTz1lztmNKksPhkMPh8Bv7+te/fqGnctFMnDiRSWwD18serteF41rZw/Wyh+t14UK5VtHR0eetsfUpoaioKLlcLnk8Hr9xj8ejjIyMoPukp6cH1Dc0NCgtLU2RkZHnrDnbMQEAwKXF9i2hoqIi5eTkKC0tTenp6dq4caM6OzuVl5cn6fStmqNHj2rr1q2SpLy8PD3zzDMqKirS/fffr+bmZtXW1vp9+ufhhx/WLbfcoj/84Q9atGiRXnzxRb388st6/fXXL9JpAgCAscx2YMnOzlZfX59Wr16t7u5upaamqr6+XomJiZKk7u5uv+9kSU5OVn19vQoLC7VhwwbFx8dr/fr1vo80S1JGRoa2b9+ulStXatWqVbrmmmtUV1enm2666SKc4shwOBwqKysLuC2F4Lhe9nC9LhzXyh6ulz1crws30tcqzLLO9zkiAACA0cWvNQMAAOMRWAAAgPEILAAAwHgEFgAAYDwCS4iqqqqUnJwsp9Mpl8ul/fv3j3ZLRnr00UcVFhbmt8XFxY12W0Z47bXXdPvttys+Pl5hYWH685//7Pe8ZVl69NFHFR8fr8suu0w//OEP9e67745OswY43/X61a9+FTDXvv/9749Os6OsvLxc3/3ud3XFFVfoqquu0p133qn33nvPr4b59bkLuV7Mr9Oqq6t1ww03+L4cLj09XX/72998z4/kvCKwhKCurk4FBQUqLS1VW1ubMjMzlZWV5fdxbnzuW9/6lrq7u33boUOHRrslI3z22WeaPXu2nnnmmaDPP/HEE6qoqNAzzzyjf/zjH4qLi9O8efN0/Pjx/3GnZjjf9ZKkH//4x35zrb6+/n/YoTkaGxv14IMP6s0335TH49GpU6fkdrv12Wef+WqYX5+7kOslMb8k6eqrr9batWvV0tKilpYW3XrrrVq0aJEvlIzovDrnLw0hqO9973tWXl6e39jMmTOt4uLiUerIXGVlZdbs2bNHuw3jSbJ27drlezw8PGzFxcVZa9eu9Y3997//taKjo62amppR6NAsX75elmVZ9957r7Vo0aJR6cd0PT09liSrsbHRsizm1/l8+XpZFvPrXCZNmmQ9++yzIz6vWGGxaXBwUK2trXK73X7jbrdbTU1No9SV2T744APFx8crOTlZd911lz788MPRbsl47e3t8nq9fvPM4XBozpw5zLNz2Ldvn6666ipde+21uv/++9XT0zPaLRnh2LFjkqQrr7xSEvPrfL58vc5gfvkbGhrS9u3b9dlnnyk9PX3E5xWBxabe3l4NDQ0F/DBjbGxswA84Qrrpppu0detW7dmzR5s2bZLX61VGRob6+vpGuzWjnZlLzLMLl5WVpW3btunVV1/VU089pX/84x+69dZbNTAwMNqtjSrLslRUVKSbb75Zqampkphf5xLseknMry86dOiQLr/8cjkcDuXl5WnXrl2aNWvWiM8r21/Nj9PCwsL8HluWFTCG0/+Rn3H99dcrPT1d11xzjf70pz+pqKhoFDsbG5hnFy47O9v359TUVKWlpSkxMVG7d+/Wz372s1HsbHQ99NBD+uc//xn0t9mYX4HOdr2YX5+77rrrdPDgQf3nP//Rjh07dO+996qxsdH3/EjNK1ZYbIqJiVF4eHhAWuzp6QlIlQj0ta99Tddff70++OCD0W7FaGc+ScU8C93UqVOVmJh4Sc+13/zmN3rppZe0d+9eXX311b5x5ldwZ7tewVzK8ysqKkrf+MY3lJaWpvLycs2ePVtPP/30iM8rAotNUVFRcrlc8ng8fuMej0cZGRmj1NXYMTAwoMOHD2vq1Kmj3YrRkpOTFRcX5zfPBgcH1djYyDy7QH19ferq6rok55plWXrooYe0c+dOvfrqq0pOTvZ7nvnl73zXK5hLeX59mWVZGhgYGPl59ZXftnsJ2r59uxUZGWnV1tZa//rXv6yCggLra1/7mtXR0THarRnnt7/9rbVv3z7rww8/tN58803rJz/5iXXFFVdwrSzLOn78uNXW1ma1tbVZkqyKigqrra3NOnLkiGVZlrV27VorOjra2rlzp3Xo0CHr7rvvtqZOnWr19/ePcuej41zX6/jx49Zvf/tbq6mpyWpvb7f27t1rpaenW9OmTbskr9cDDzxgRUdHW/v27bO6u7t924kTJ3w1zK/Pne96Mb8+V1JSYr322mtWe3u79c9//tNasWKFNWHCBKuhocGyrJGdVwSWEG3YsMFKTEy0oqKirO985zt+H3/D57Kzs62pU6dakZGRVnx8vPWzn/3Mevfdd0e7LSPs3bvXkhSw3XvvvZZlnf7oaVlZmRUXF2c5HA7rlltusQ4dOjS6TY+ic12vEydOWG6325oyZYoVGRlpTZ8+3br33nutzs7O0W57VAS7TpKsP/7xj74a5tfnzne9mF+fu++++3z/9k2ZMsW67bbbfGHFskZ2XoVZlmV99XUaAACAkcN7WAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAw3v8Hm6nnv7pBWZ8AAAAASUVORK5CYII=\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# We can now plot it simply by\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Simply call a barplot\\n\",\n \"plt.bar(k,pmf_pois)\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the question: What is the probability that more than 10 customers arrive? We need to sum up the value of every bar past 10 the 10 customers bar.\\n\",\n \"\\n\",\n \"We can do this by using a Cumulative Distribution Function (CDF). This describes the probability that a random variable X with a given probability distribution (such as the Poisson in this current case) will be found to have a value less than or equal to X.\\n\",\n \"\\n\",\n \"What this means is if we use the CDF to calcualte the probability of 10 or less customers showing up we can take that probability and subtract it from the total probability space, which is just 1 (the sum of all the probabilities for every number of customers).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability that 10 or less customers show up is 58.3 %.\\n\"\n ]\n }\n ],\n \"source\": [\n \"# scipy has a built in cdf we can use\\n\",\n \"\\n\",\n \"# Set out k = 10 for ten customers, set mean = 10 for the average of ten customers during lunch rush.\\n\",\n \"k,mu = 10,10\\n\",\n \"\\n\",\n \"# The probability that 10 or less customers show up is:\\n\",\n \"prob_up_to_ten = poisson.cdf(k,mu)\\n\",\n \"\\n\",\n \"#print\\n\",\n \"print( 'The probability that 10 or less customers show up is %2.1f %%.' %(100*prob_up_to_ten))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can answer the question for *more than* 10 customers. It will be the remaining probability space\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability that more than ten customers show up during lunch rush is 41.7 %.\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Sorry for the long object names, but hopefully this makes the thought process very clear\\n\",\n \"prob_more_than_ten = 1 - prob_up_to_ten\\n\",\n \"\\n\",\n \"print( 'The probability that more than ten customers show up during lunch rush is %2.1f %%.' %(100*prob_more_than_ten))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"-----\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"That's it for the basics of the poisson distribution! More free info can be found at these sources:\\n\",\n \"\\n\",\n \"1.)http://en.wikipedia.org/wiki/Poisson_distribution#Definition\\n\",\n \"\\n\",\n \"2.)http://stattrek.com/probability-distributions/poisson.aspx\\n\",\n \"\\n\",\n \"3.)http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Sampling Techniques-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about sampling theory!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Sampling Theory is a study of relationships exisiting between a population and the samples drawn from the population. For instance, the population may be the entire population of the United States, while the sample may be 1000 people you polled for a survey.\\n\",\n \"\\n\",\n \"There are a ton of important questions we want to ask pertaining to sampling theory, such as whether the observed difference between two samples are due to chance variation or if they are statistically significant. These are sometimes known as *tests of significance*. We'll talk about them later in another iPython notebook.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Random Samples and Numbers\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Samples must be chosen so that they are representative of a population. One method of doing this is by selecting using *random sampling*. This methods means that every member of the population has an euqal chance of being selected. There's lots of ways to create a \\\"random\\\" sampling method, it can be as simple as picking names from a hat, or using pseudorandom number generators such as a Mersenne Twister (the default PRNG for python).\\n\",\n \"\\n\",\n \"Learn more about it at (python 2): https://docs.python.org/2/library/random.html\\n\",\n \"\\n\",\n \"Learn more about it at (python 3): https://docs.python.org/3/library/random.html\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling with and without Replacement\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Drawing samples without replacement from a finite source of samples is considered a finite sampling. Drawing samples from a finite source with replacement can be considered infinite. Such as tossing a coin N number of times, while there are only two possibile outcomes, there is an infinite possibility of any series of heads or tails as N goes to infinity.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Means\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you draw N samples from a finite population of Np samples where Np>N then the mean and the std are denoted as the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean: $$\\\\mu_x=\\\\mu$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation: $$\\\\sigma_x= \\\\frac{\\\\sigma}{\\\\sqrt{N}}\\\\sqrt{ \\\\frac{N_p-N}{N_p-N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that we can relate our mean and std from out sample to the total sample population.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Proportions\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If the population is infinite and the probability of succes is denoted as p and probability of failure is q=1-p (just like in a binomial distirbution, like a coin flip). The sampling distribution of proportions then has a mean and standard deviation notes as the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean: $$\\\\mu_p=p$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation: $$\\\\sigma_p=\\\\sqrt{\\\\frac{pq}{N}}=\\\\sqrt{\\\\frac{p(1-p)}{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Differences and Sums\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you are given two sample populations N1 and N2 both of which are normally distributed, we can obtain the mean and standard deviation of the sampling distribution of diffrences or sums of the statistics. If S1 is a statistics of N1 and S2 a statistic of N2 we can obtain the mean and standard deviation as follows:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the *differences of the statistics* :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is: $$\\\\mu_{S1-S2}=\\\\mu_{S1}-\\\\mu_{S2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation is: $$ \\\\sigma_{S1-S2}=\\\\sqrt{{\\\\sigma^2}_{S1}+{\\\\sigma^2}_{S2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the *sum of the statistics* :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is: $$\\\\mu_{S1-S2}=\\\\mu_{S1}+\\\\mu_{S2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation is: $$ \\\\sigma_{S1-S2}=\\\\sqrt{{\\\\sigma^2}_{S1}+{\\\\sigma^2}_{S2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Notice that the standard deviations are summed for both cases, but the means are not!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This is just a quick intro to the topic of sampling theory, check out more here:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Sampling_distribution\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": ".ipynb_checkpoints/Statistical Estimation Theory-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/Statistics Overview-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#APPENDIX B- STATISTICS OVERVIEW\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Overview of main topic\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##Example problem or manual creation of distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Use scipy to create or analyze the statistics\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##Additional resources for learning more about the topic\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The online notebooks can be viewed here:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"http://nbviewer.ipython.org/github/jmportilla/Statistics-Notes/tree/master/\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": ".ipynb_checkpoints/T Distribution (Small Sampling Theory)-checkpoint.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn the T-distribution! Note: Learn about the normal distribution first!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For previous distributions the sample size was assumed large (N>30). For sample sizes that are less than 30, otherwise (N<30). Note: Sometimes the t-distribution is known as the student distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The t-distribution allows for use of small samples, but does so by sacrificing certainty with a margin-of-error trade-off. The t-distribution takes into account the sample size using n-1 degrees of freedom, which means there is a different t-distribution for every different sample size. If we see the t-distribution against a normal distribution, you'll notice the tail ends increase as the peak get 'squished' down. \\n\",\n \"\\n\",\n \"It's important to note, that as n gets larger, the t-distribution converges into a normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To further explain degrees of freedom and how it relates tothe t-distribution, you can think of degrees of freedom as an adjustment to the sample size, such as (n-1). This is connected to the idea that we are estimating something of a larger population, in practice it gives a slightly larger margin of error in the estimate.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's define a new variable called t, where\\n\",\n \":\\n\",\n \"$$t=\\\\frac{\\\\overline{X}-\\\\mu}{s}\\\\sqrt{N-1}=\\\\frac{\\\\overline{X}-\\\\mu}{s/\\\\sqrt{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"which is analogous to the z statistic given by $$z=\\\\frac{\\\\overline{X}-\\\\mu}{\\\\sigma/\\\\sqrt{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The sampling distribution for t can be obtained:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"## $$ f(t) = \\\\frac {\\\\varGamma(\\\\frac{v+1}{2})}{\\\\sqrt{v\\\\pi}\\\\varGamma(\\\\frac{v}{2})} (1+\\\\frac{t^2}{v})^{-\\\\frac{v+1}{2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where the gamma function is: $$\\\\varGamma(n)=(n-1)!$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And v is the number of degrees of freedom, typically equal to N-1. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Similar to a z-score table used with a normal distribution, a t-distribution uses a t-table. Knowing the degrees of freedom and the desired cumulative probability (e.g. P(T >= t) ) we can find the value of t. Here is an example of a lookup table for a t-distribution: \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to get the t-distribution in Python using scipy!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 15,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Import for plots\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Import the stats library\\n\",\n \"from scipy.stats import t\\n\",\n \"\\n\",\n \"#import numpy\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Create x range\\n\",\n \"x = np.linspace(-5,5,100)\\n\",\n \"\\n\",\n \"# Create the t distribution with scipy\\n\",\n \"rv = t(3)\\n\",\n \"\\n\",\n \"# Plot the PDF versus the x range\\n\",\n \"plt.plot(x, rv.pdf(x))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Additional resources can be found here:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Student%27s_t-distribution\\n\",\n \"\\n\",\n \"2.) http://mathworld.wolfram.com/Studentst-Distribution.html\\n\",\n \"\\n\",\n \"3.) http://stattrek.com/probability-distributions/t-distribution.aspx\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Bayes' Theorem.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"source\": [\n \"# Bayes Theorem\\n\",\n \"\\n\",\n \"In this Statistics Notebook we will be going over Bayes Theorem and an example of how to use it. This theorem will be important to understand in many situations and we will be using it for Machine Learning in certain lectures.\\n\",\n \"\\n\",\n \"We will start by describing the equation for Bayes Theorem and then complete an example problem. There won't be a SciPy portion to this lecture because this is really more of a math overview than a discussion on a distribution.\\n\",\n \"\\n\",\n \"### Overview\\n\",\n \"\\n\",\n \"In probability theory and statistics, Bayes' theorem describes the probability of an event, based on conditions that might be related to the event. Bayes Theorem allows us to use previously known information to asess likelihood of another related event.\\n\",\n \"\\n\",\n \"You will usually see Bayes Theorem displayed in one of two ways:\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B)} $$\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B|A)P(A) + P(B|not A)P(not A)}$$\\n\",\n \"\\n\",\n \"Here P(A|B) stands for the Probability that A happened given B has occured. These are both the same, in the second case, you would use this form if you don't directly have the Probability of B occuring on its own.\\n\",\n \"\\n\",\n \"Let's go ahead and dive into an example Problem to see how to use Baye's Theorem!\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Example Problem\\n\",\n \"\\n\",\n \"This is a classic example of Bayes Theorem:\\n\",\n \"\\n\",\n \"We have a test to screen for breast cancer, with the following conditions:\\n\",\n \"\\n\",\n \"- 1% of women have breast cancer \\n\",\n \"- 80% of mammograms detect breast cancer when it is there\\n\",\n \"- 9.6 % of mammograms detect breast cancer when it is *not* there. (False Positive)\\n\",\n \"\\n\",\n \"We could assign the probabilities to the sample space by using a table:\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"
Cancer (1%)No Cancer (99%)
Tested Positive80%9.6%
Tested Negative20%90.4%
\\n\",\n \"\\n\",\n \"\\n\",\n \"Now let's say you wanted to know how accurate this test is. If someone went to go get the test and had a positive result, what is the probability that they have breast cancer?\\n\",\n \"\\n\",\n \"We can first visualize Bayes Theorem by filling out the table above:\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"
Cancer (1%)No Cancer (99%)
Tested PositiveTrue Positive: 1% × 80%False Positive: 99% × 9.6%
Tested NegativeFalse Negative: 1% × 20%True Negative: 99% × 90.4%
\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Remember that the proabbility of an event occuring is the number of ways it could happen given all possible outcomes:\\n\",\n \"\\n\",\n \"$$ Probability = \\\\frac{Desired \\\\ event} { All \\\\ possibilities}$$\\n\",\n \"\\n\",\n \"Then the probability of getting a real, positive result is .01 × .8 = .008. \\n\",\n \"\\n\",\n \"The chance of getting any type of positive result is the chance of a *true positive* plus the chance of a *false positive* \\n\",\n \"which is (.008 + 0.09504 = .10304).\\n\",\n \"\\n\",\n \"So, our chance of cancer is .008/.10304 = 0.0776, or about 7.8%.\\n\",\n \"\\n\",\n \"This means that a positive mammogram results in only a 7.8% chance of cancer, rather than 80% (the supposed accuracy of the test). \\n\",\n \"\\n\",\n \"This might seem counter intuitive at first but it makes sense: the test gives a false positive 10% of the time, so there will be a ton of false positives in any given population. There will be so many false positives, in fact, that most of the positive test results will be wrong.\\n\",\n \"\\n\",\n \"Now we can turn the above process into the Bayes Theorem Equation:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's go ahead and plug in the information we do know into the second equation.\\n\",\n \"\\n\",\n \"$$ P(A|B) = \\\\frac{P(B|A)P(A)}{P(B|A)P(A) + P(B|not A)P(not A)}$$\\n\",\n \"\\n\",\n \"Looking back on the information we were given:\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(A|B) = Chance of having cancer (A) given a positive test (B). This is the desired information: How likely is it to have cancer with a positive result? We've already solved it using the table, so let's see if the equation agrees with our results: 7.8%.\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(B|A) = Chance of a positive test (B) given that you had cancer (A). This is the chance of a true positive, 80% in this case.\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(A) = Chance of having cancer (1%).\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(not A) = Chance of not having cancer (99%).\\n\",\n \"\\n\",\n \"\\n\",\n \"* Pr(B|not A) = Chance of a positive test (B) given that you didn’t have cancer ( Not A). This is a false positive, 9.6% in our case.\\n\",\n \"\\n\",\n \"Plugging in these numbers, we arrive at the same answer as our table method: 7.76%\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Other great resources for more on Bayes Theorem:\\n\",\n \"\\n\",\n \"1.) [Simple Explanation using Legos](https://www.countbayesie.com/blog/2015/2/18/bayes-theorem-with-lego)\\n\",\n \"\\n\",\n \"2.) [Wikipedia](http://en.wikipedia.org/wiki/Bayes%27_theorem)\\n\",\n \"\\n\",\n \"3.) [Stat Trek](http://stattrek.com/probability/bayes-theorem.aspx)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Bayseian A-B Testing.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Beta Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"####Let's learn the Beta distribution!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true\n },\n \"source\": [\n \"The beta distribution is a continuous distribution which can take values between 0 and 1. This distribution is parameterized by \\n\",\n \"two shape parameters α and β.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"import seaborn as sns\\n\",\n \"\\n\",\n \"from scipy import stats\\n\",\n \"\\n\",\n \"a = 0.5\\n\",\n \"b = 0.5\\n\",\n \"x = np.arange(0.01,1,0.01)\\n\",\n \"y = stats.beta.pdf(x,a,b)\\n\",\n \"plt.plot(x,y)\\n\",\n \"plt.title('Beta: a=%.1f,b=%.1f' %(a,b))\\n\",\n \"\\n\",\n \"plt.xlabel('x')\\n\",\n \"plt.ylabel('Probability density')\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Binomial Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Binomial is a specific type of a discrete probability distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's see an example question first, and then learn about the binomial distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Example 1: Two players are playing basketball, player A and player B. Player A takes an average of 11 shots per game, and \\n\",\n \"has an average success rate of 72%. Player B takes an average of 15 shots per game, but has an average success rate of 48%.\\n\",\n \"\\n\",\n \"Question 1: What's the probability that Player A makes 6 shots in an average game?\\n\",\n \"\\n\",\n \"Question 2: What's the probability that Player B makes 6 shots in an average game?\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can classify this as a binomial experiment if the following conditions are met:\\n\",\n \" \\n\",\n \" 1.) The process consists of a sequence of n trials.\\n\",\n \" 2.) Only two exclusive outcomes are possible for each trial (A success and a failure)\\n\",\n \" 3.) If the probability of a success is 'p' then the probability of failure is q=1-p\\n\",\n \" 4.) The trials are independent.\\n\",\n \" \\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The formula for a Binomial Distribution Probability Mass Function turns out to be: \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$Pr(X=k)=C(n,k)p^k (1-p)^{n-k}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where n= number of trials,k=number of successes,p=probability of success,1-p=probability of failure (often written as q=1-p).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that to get exactly 'k' successes in 'n' trials, we want exactly 'k' successes: $$p^k$$ \\n\",\n \"and we want 'n-k' failures:$$(1-p)^{n-k}$$\\n\",\n \"Then finally, there are $$C(n,k)$$ ways of putting 'k' successes in 'n' trials.\\n\",\n \"So we multiply all these together to get the probability of exactly that many success and failures in those n trials!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"--------------------------------------------------------------------------------------------------------------------------------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Quick note, C(n,k) refers to the number of possible combinations of N things taken k at a time.\\n\",\n \"\\n\",\n \"This is also equal to: $$C(n,k) = \\\\frac{n!}{k!(n-k)!}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### So let's try out the example problem!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" The probability of player A making 6 shots in an average game is 11.1% \\n\",\n \" \\n\",\n \"\\n\",\n \" The probability of player B making 6 shots in an average game is 17.0% \\n\"\n ]\n }\n ],\n \"source\": [\n \"# Set up player A\\n\",\n \"\\n\",\n \"# Probability of success for A\\n\",\n \"p_A = .72\\n\",\n \"# Number of shots for A\\n\",\n \"n_A = 11\\n\",\n \"\\n\",\n \"# Make 6 shots\\n\",\n \"k = 6\\n\",\n \"\\n\",\n \"# Now import scipy for combination\\n\",\n \"import scipy.special as sc\\n\",\n \"\\n\",\n \"# Set up C(n,k)\\n\",\n \"comb_A = sc.comb(n_A,k)\\n\",\n \"\\n\",\n \"# Now put it together to get the probability!\\n\",\n \"answer_A = comb_A * (p_A**k) * ((1-p_A)**(n_A-k))\\n\",\n \"\\n\",\n \"# Put the answer in percentage form!\\n\",\n \"answer_A = 100*answer_A\\n\",\n \"\\n\",\n \"\\n\",\n \"# Quickly repeat all steps for Player B\\n\",\n \"p_B = .48\\n\",\n \"n_B = 15\\n\",\n \"comb_B = sc.comb(n_B,k)\\n\",\n \"answer_B = 100 * comb_B * (p_B**k) * ((1-p_B)**(n_B-k))\\n\",\n \"\\n\",\n \"\\n\",\n \"#Print Answers\\n\",\n \"print( ' The probability of player A making 6 shots in an average game is %1.1f%% ' %answer_A)\\n\",\n \"print( ' \\\\n')\\n\",\n \"print( ' The probability of player B making 6 shots in an average game is %1.1f%% ' %answer_B)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now we know that even though player B is technically a worse shooter, because she takes more shots she will have a higher chance of making 6 shots in an average game!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"But wait a minute... what about a higher amount of shots, will player's A higher probability take a stronger effect then?\\n\",\n \"What's the probability of making 9 shots a game for either player?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 44,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" \\n\",\n \"\\n\",\n \" The probability of player A making 9 shots in an average game is 22.4% \\n\",\n \"\\n\",\n \"\\n\",\n \" The probability of player B making 9 shots in an average game is 13.4% \\n\",\n \"\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"#Let's find out!\\n\",\n \"\\n\",\n \"#Set number of shots\\n\",\n \"k = 9\\n\",\n \"\\n\",\n \"#Set new combinations\\n\",\n \"comb_A = sc.comb(n_A,k)\\n\",\n \"comb_B = sc.comb(n_B,k)\\n\",\n \"\\n\",\n \"# Everything else remains the same\\n\",\n \"answer_A = 100 * comb_A * (p_A**k) * ((1-p_A)**(n_A-k))\\n\",\n \"answer_B = 100 * comb_B * (p_B**k) * ((1-p_B)**(n_B-k))\\n\",\n \"\\n\",\n \"#Print Answers\\n\",\n \"print( ' \\\\n')\\n\",\n \"print( ' The probability of player A making 9 shots in an average game is %1.1f%% ' %answer_A)\\n\",\n \"print( '\\\\n')\\n\",\n \"print( ' The probability of player B making 9 shots in an average game is %1.1f%% ' %answer_B)\\n\",\n \"print( '\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we see that player's A ability level gives better odds of making exactly 9 shots. We need to keep in mind that we are asking\\n\",\n \"about the probability of making *exactly* those amount of shots. This is a different question than \\\" What's the probability that player A makes *at least* 9 shots?\\\".\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Now let's investigate the mean and standard deviation for the binomial distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean of a binomial distribution is simply: $$\\\\mu=n*p$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This intuitively makes sense, the average number of successes should be the total trials multiplied by your average success rate.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Similarly we can see that the standard deviation of a binomial is: $$\\\\sigma=\\\\sqrt{n*q*p}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now we can ask, whats the average number of shots each player will make in a game +/- a standard distribution?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 52,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\n\",\n \"\\n\",\n \"Player A will make an average of 8 +/- 1 shots per game\\n\",\n \"\\n\",\n \"\\n\",\n \"Player B will make an average of 7 +/- 2 shots per game\\n\",\n \"\\n\",\n \"\\n\",\n \"NOTE: It's impossible to make a decimal of a shot so '%1.0f' was used to replace the float!\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Let's go ahead and plug in to the formulas.\\n\",\n \"\\n\",\n \"# Get the mean\\n\",\n \"mu_A = n_A *p_A\\n\",\n \"mu_B = n_B *p_B\\n\",\n \"\\n\",\n \"#Get the standard deviation\\n\",\n \"sigma_A = ( n_A *p_A*(1-p_A) )**0.5\\n\",\n \"sigma_B = ( n_B *p_B*(1-p_B) )**0.5\\n\",\n \"\\n\",\n \"# Now print results\\n\",\n \"print( '\\\\n')\\n\",\n \"print( 'Player A will make an average of %1.0f +/- %1.0f shots per game' %(mu_A,sigma_A))\\n\",\n \"print( '\\\\n')\\n\",\n \"print( 'Player B will make an average of %1.0f +/- %1.0f shots per game' %(mu_B,sigma_B))\\n\",\n \"print( '\\\\n')\\n\",\n \"print( \\\"NOTE: It's impossible to make a decimal of a shot so '%1.0f' was used to replace the float!\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's see how to automatically make a binomial distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 60,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"7.92\\n\",\n \"1.4891608375189027\\n\"\n ]\n }\n ],\n \"source\": [\n \"from scipy.stats import binom\\n\",\n \"\\n\",\n \"# We can get stats: Mean('m'), variance('v'), skew('s'), and/or kurtosis('k')\\n\",\n \"mean,var= binom.stats(n_A,p_A)\\n\",\n \"\\n\",\n \"print( mean)\\n\",\n \"print( var**0.5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Looks like it matches up with our manual methods. Note: we did not round in this case.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### We can also get the probability mass function:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's try another example to see the full PMF (Probability Mass Function) and plotting it.\\n\",\n \"\\n\",\n \"Imagine you flip a fair coin. Your probability of getting a heads is p=0.5 (success in this example).\\n\",\n \"\\n\",\n \"So what does your probability mass function look like for 10 coin flips?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 65,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"array([0.00097656, 0.00976563, 0.04394531, 0.1171875 , 0.20507812,\\n\",\n \" 0.24609375, 0.20507812, 0.1171875 , 0.04394531, 0.00976563,\\n\",\n \" 0.00097656])\"\n ]\n },\n \"execution_count\": 65,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Set up a new example, let's say n= 10 coin flips and p=0.5 for a fair coin.\\n\",\n \"n=10\\n\",\n \"p=0.5\\n\",\n \"\\n\",\n \"# Set up n success, remember indexing starts at 0, so use n+1\\n\",\n \"x = range(n+1)\\n\",\n \"\\n\",\n \"# Now create the probability mass function\\n\",\n \"Y = binom.pmf(x,n,p)\\n\",\n \"\\n\",\n \"#Show\\n\",\n \"Y\\n\",\n \"\\n\",\n \"# Next we'll visualize the pmf by plotting it.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Finally, let's plot the binomial distribution to get the full picture.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 77,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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L1yeTdY0qA8zwJJ35C0bq7d7ZbPSSQdXYmF1OQYwDuS9pO0e07mC0hJ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\\n\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"# For simple plots, matplotlib is fine, seaborn is unnecessary.\\n\",\n \"\\n\",\n \"# Now simply use plot\\n\",\n \"plt.plot(x,Y,'o')\\n\",\n \"\\n\",\n \"#Title (use y=1.08 to raise the long title a little more above the plot)\\n\",\n \"plt.title('Binomial Distribution PMF: 10 coin Flips, Odds of Success for Heads is p=0.5',y=1.08)\\n\",\n \"\\n\",\n \"#Axis Titles\\n\",\n \"plt.xlabel('Number of Heads')\\n\",\n \"plt.ylabel('Probability')\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"That's it for the review on Binomial Distributions. More info can be found at the following sources:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Binomial_distribution\\n\",\n \"\\n\",\n \"2.) http://stattrek.com/probability-distributions/binomial.aspx\\n\",\n \"\\n\",\n \"3.) http://mathworld.wolfram.com/BinomialDistribution.html\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Thanks!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Chi-Square.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Chi-Square\\n\",\n \"\\n\",\n \"In this Statistics Appendix Lecture, we'll go over the Chi-Square Distribution and the Chi-Square Test. \\n\",\n \"\\n\",\n \"*Note: Before viewing this lecture, see the Hypothesis Testing Notebook Lecture.*\\n\",\n \"\\n\",\n \"Let's start by introducing the general idea of observed and theoretical frequencies, then later we'll approach the idea of the Chi-Sqaure Distribution and its definition. After that we'll do a qcuik example with Scipy on using the Chi-Square Test.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Supppose that you tossed a coin 100 times. Theoretically you would expect 50 tails and 50 heads, however it is pretty unlikely you get that result exactly. Then a question arises... how far off from you expected/theoretical frequency would you have to be in order to conclude that the observed result is statistically significant and is not just due to random variations.\\n\",\n \"\\n\",\n \"We can begin to think about this question by defining an example set of possible events. We'll call them Events 1 through *k*. Each of these events has an expected (theoretical) frequency and an observed frequency. We can display this as a table:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
EventEvent 1Event 2Event 3...Event k
Observed Frequency$$o_1$$$$o_2$$$$o_3$$...$$o_k$$
Expected Frequency$$e_1$$$$e_2$$$$e_3$$...$$e_k$$
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Since we wanted to know whether observed frequencies differ significantly from the expected frequencies we'll have to define a term for a measure of discrepency.\\n\",\n \"\\n\",\n \"We'll define this measure as Chi-Square, which will be the sum of the squared difference between the observed and expected frequency divided by the expected frequency for all events. To show this more clearly, this is mathematically written as:\\n\",\n \"$$ \\\\chi ^2 = \\\\frac{(o_1 - e_1)^2}{e_1}+\\\\frac{(o_2 - e_2)^2}{e_2}+...+\\\\frac{(o_k - e_k)^2}{e_k} $$\\n\",\n \"Which is the same as:\\n\",\n \"$$\\\\chi ^2 = \\\\sum^{k}_{j=1} \\\\frac{(o_j - e_j)^2}{e_j} $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If the total frequency is N\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sum o_j = \\\\sum e_j = N $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Then we could rewrite the Chi-Square Formula to be:\\n\",\n \"$$ \\\\chi ^2 = \\\\sum \\\\frac{o_j ^2}{e_j ^2} - N$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can now see that if the Chi Square value is equal to zero, then the observed and theoretical frequencies agree exactly. While if the Chi square value is greater than zero, they do not agree.\\n\",\n \"\\n\",\n \"The sampling distribution of Chi Square is approximated very closely by the *Chi-Square distribution*\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The Chi Square Distribution\\n\",\n \"\\n\",\n \"The Chi-Square Distribution is related to the standard normal distribution. If a random variable Z, then Z2 has the Chi Square distribution with one degree of freedom. This idea is best presented graphically in a video. I've embedded a video below which goes over this an a way better than this static iPython Notebook format.\\n\",\n \"\\n\",\n \"Here is an excellent video explaining the basics of the Chi Square Distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\"text/html\": [\n \"\\n\",\n \" \\n\",\n \" \"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import YouTubeVideo\\n\",\n \"YouTubeVideo(\\\"hcDb12fsbBU\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The Chi Square Test for Goodness of Fit\\n\",\n \"\\n\",\n \"We can now use the [Chi-Square test](http://stattrek.com/chi-square-test/goodness-of-fit.aspx?Tutorial=AP) can be used to determine how well a theoretical distribution fits an observed empirical distribution. \\n\",\n \"\\n\",\n \"Scipy will basically be constructing and looking up this table for us:\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 12,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url='http://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Chi-square_distributionCDF-English.png/300px-Chi-square_distributionCDF-English.png'\\n\",\n \"\\n\",\n \"from IPython.display import Image\\n\",\n \"Image(url)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"Let's go ahead and do an example problem. Say you are at a casino and are in charge of monitoring a [craps](http://en.wikipedia.org/wiki/Craps)(a dice game where two dice are rolled). You are suspcious that a player may have switched out the casino's dice for their own. How do we use the Chi-Square test to check whether or not this player is cheating?\\n\",\n \"\\n\",\n \"You will need some observations in order to begin. You begin to keep track of this player's roll outcomes.You record the next 500 rolls taking note of the sum of the dice roll result and the number of times it occurs.\\n\",\n \"\\n\",\n \"You record the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
Sum of Dice Roll23456789101112
Number of Times Observed83248596784765734287
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we also know the espected frequency of these sums for a fair dice. That frequency distribution looks like this:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
Sum of Dice Roll23456789101112
Expected Frequency1/362/363/364/365/366/365/364/363/362/361/36
\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can calculated the expected number of rolls by multiplying the expected frequency with the total sum of the rolls (500 rolls).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"500\"\n ]\n },\n \"execution_count\": 20,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# Check sum of the rolls\\n\",\n \"observed = [8,32,48,59,67,84,76,57,34,28,7]\\n\",\n \"roll_sum = sum(observed)\\n\",\n \"roll_sum\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[0.027777777777777776,\\n\",\n \" 0.05555555555555555,\\n\",\n \" 0.08333333333333333,\\n\",\n \" 0.1111111111111111,\\n\",\n \" 0.1388888888888889,\\n\",\n \" 0.16666666666666666,\\n\",\n \" 0.1388888888888889,\\n\",\n \" 0.1111111111111111,\\n\",\n \" 0.08333333333333333,\\n\",\n \" 0.05555555555555555,\\n\",\n \" 0.027777777777777776]\"\n ]\n },\n \"execution_count\": 22,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# The expected frequency\\n\",\n \"freq = [1,2,3,4,5,6,5,4,3,2,1]\\n\",\n \"\\n\",\n \"# Note use of float for python 2.7\\n\",\n \"possible_rolls = 1.0/36\\n\",\n \"\\n\",\n \"freq = [possible_rolls*dice for dice in freq]\\n\",\n \"\\n\",\n \"#Check\\n\",\n \"freq\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Excellent, now let's multiply our frequency by the sum to get the expected number of rolls for each frequency.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[13.888888888888888,\\n\",\n \" 27.777777777777775,\\n\",\n \" 41.666666666666664,\\n\",\n \" 55.55555555555555,\\n\",\n \" 69.44444444444444,\\n\",\n \" 83.33333333333333,\\n\",\n \" 69.44444444444444,\\n\",\n \" 55.55555555555555,\\n\",\n \" 41.666666666666664,\\n\",\n \" 27.777777777777775,\\n\",\n \" 13.888888888888888]\"\n ]\n },\n \"execution_count\": 25,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"expected = [roll_sum*f for f in freq]\\n\",\n \"expected\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can now use Scipy to perform the [Chi Square Test](http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.chisquare.html) by using chisquare.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The chi-squared test statistic is 9.89\\n\",\n \"The p-value for the test is 0.45\\n\"\n ]\n }\n ],\n \"source\": [\n \"from scipy import stats\\n\",\n \"\\n\",\n \"chisq,p = stats.chisquare(observed,expected)\\n\",\n \"\\n\",\n \"print( 'The chi-squared test statistic is %.2f' %chisq)\\n\",\n \"print( 'The p-value for the test is %.2f' %p)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"stats.chisquare returns two values, the chi-squared test statistic and the p-value of the test.\\n\",\n \"\\n\",\n \"With such a high p-value, we have no reason to doubt the fairness of the dice.\\n\",\n \"\\n\",\n \"That's it for the Chi-Square Distirbution and Test!\\n\",\n \"\\n\",\n \"For more information, check out these links:\\n\",\n \"\\n\",\n \"1. [Wikipedia](http://en.wikipedia.org/wiki/Chi-squared_test)\\n\",\n \"\\n\",\n \"2. [Stat trek](http://stattrek.com/chi-square-test/independence.aspx)\\n\",\n \"\\n\",\n \"3. [Khan Academy](https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/pearson-s-chi-square-test-goodness-of-fit)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Continuous Uniform Distributions.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about Continous Uniform Distributions. Note: You should look at Discrete Uniform Distributions first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we took a discrete uniform distribution to probability of any outcome was 1/n for any outcome, however for a *continous* distribution, our data can not be divided in discrete components, for example weighing an object. With perfect precision on weight, the data can take on any value between two points(e.g 5.4 grams,5.423 grams, 5.42322 grams, etc.) \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that our n possible values from the discrete uniform distribution is going towards infinity, thus the probability of any *individual* outcome for a continous distribution is 1/∞ ,technically undefined or zero if we take the limit to infinity. Thus we can only take probability measurements of ranges of values, and not just a specific point. Let's look at some definitions and examples to get a better understanding!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##### A continous random variable X with a probability density function is a continous uniform random variable when:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$f(x)=\\\\frac{1}{(b-a)}\\\\\\\\\\\\\\\\a<=x<=b$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This makes sense, since for a discrete uniform distribution the f(x)=1/n but in the continous case we don't have a specific n possibilities, we have a range from the min (a) to the max (b)!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is simply the average of the min and max:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$\\\\frac{(a+b)}{2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The variance is defined as:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sigma^2 = \\\\frac{(b-a)^2}{12}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what would an example problem look like? Let's say on average, a taxi ride in NYC takes 22 minutes. After taking some time measurements from experiments we gather that all the taxi rides are uniformly distributed between 19 and 27 minutes. What is the probability density function of a taxi ride, or f(x)?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability density function results in 0.125\\n\"\n ]\n }\n ],\n \"source\": [\n \"#Let's solve this with python\\n\",\n \"\\n\",\n \"#Lower bound time\\n\",\n \"a = 19\\n\",\n \"\\n\",\n \"#Upper bound time\\n\",\n \"b = 27\\n\",\n \"\\n\",\n \"#Then using our probability density function we get\\n\",\n \"fx = 1.0/(b-a)\\n\",\n \"\\n\",\n \"#show \\n\",\n \"print('The probability density function results in %1.3f' %fx)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The variance of the continous unifrom distribution is 5.3\\n\"\n ]\n }\n ],\n \"source\": [\n \"#We can also get the variance \\n\",\n \"var = ((b-a)**2 )/12\\n\",\n \"\\n\",\n \"#Show\\n\",\n \"print('The variance of the continous unifrom distribution is %1.1f' %var)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So let's ask the question, what's the probability that the taxi ride will last *at least* 25 minutes?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" The probability that the taxi ride will last at least 25 minutes is 25.0%\\n\"\n ]\n }\n ],\n \"source\": [\n \"# This is the same as the PDF of f(27) (the entire space) minus the probability space less than 25 minutes.\\n\",\n \"\\n\",\n \"#f(27)\\n\",\n \"fx_1 = 27.0/(b-a)\\n\",\n \"#f(25)\\n\",\n \"fx_2 = 25.0/(b-a)\\n\",\n \"\\n\",\n \"#Our answer is then\\n\",\n \"ans = fx_1-fx_2\\n\",\n \"\\n\",\n \"#print\\n\",\n \"print(' The probability that the taxi ride will last at least 25 minutes is %2.1f%%' %(100*ans))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to do this automatically with scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 37,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 37,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Import the following\\n\",\n \"from scipy.stats import uniform\\n\",\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"#Let's set an A and B\\n\",\n \"A=0\\n\",\n \"B=5\\n\",\n \"\\n\",\n \"# Set x as 100 linearly spaced points between A and B\\n\",\n \"x = np.linspace(A,B,100)\\n\",\n \"\\n\",\n \"# Use uniform(loc=start point,scale=endpoint)\\n\",\n \"rv = uniform(loc=A,scale=B)\\n\",\n \"\\n\",\n \"#Plot the PDF of that uniform distirbution\\n\",\n \"plt.plot(x,rv.pdf(x))\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Note the above line is at 0.2, as we would expect since 1/(5-0) is 1/5 or 0.2.\\n\",\n \"\\n\",\n \"####That's it for Uniform Continuous Distributions. Here are some more resource for you:\\n\",\n \"\\n\",\n \"1.)http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29\\n\",\n \"\\n\",\n \"2.)http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html\\n\",\n \"\\n\",\n \"3.)http://mathworld.wolfram.com/UniformDistribution.html\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Discrete Uniform Distributions.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Let's start off with a definition for discrete uniform distributions.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Definition: A random variable X has a discrete uniform distribution if each of the n values in its range:\\n\",\n \" x1,x2,x3....xn has equal probability:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ f(x_{i}) = 1/n $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's use python to show a simple example!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First the imports:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Import all the usual imports from the Python for Data Analysis and Visualization Course.\\n\",\n \"import numpy as np\\n\",\n \"from numpy.random import randn\\n\",\n \"import pandas as pd\\n\",\n \"from scipy import stats\\n\",\n \"import matplotlib as mpl\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"from __future__ import division\\n\",\n \"%matplotlib inline\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's set up a dice roll and plot the distribution using seaborn before we go use matplotlib by itself.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Probability Mass Function for Dice Roll')\"\n ]\n },\n \"execution_count\": 8,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# How about a roll of a dice?\\n\",\n \"\\n\",\n \"# Let's check out the Probability Mass function!\\n\",\n \"\\n\",\n \"# Each number\\n\",\n \"roll_options = [1,2,3,4,5,6]\\n\",\n \"\\n\",\n \"# Total probability space\\n\",\n \"tprob = 1\\n\",\n \"\\n\",\n \"# Each roll has same odds of appearing (on a fair die at least)\\n\",\n \"prob_roll = tprob / len(roll_options)\\n\",\n \"\\n\",\n \"# Plot using seaborn rugplot (note this is not really a rugplot), setting height equal to probability of roll\\n\",\n \"uni_plot = sns.rugplot(roll_options,height=prob_roll,c='indianred')\\n\",\n \"\\n\",\n \"# Set Title\\n\",\n \"uni_plot.set_title('Probability Mass Function for Dice Roll')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can see in the above example that the f(x) value on the plot is just equal to 1/(Total Possible Outcomes)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"-------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what's the mean and variance of this uniform distribution? \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is simply the max and min value divided by two, just like the mean of two numbers.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\mu = (b+a)/2 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"With a variance of:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ \\\\sigma^2=\\\\frac{(b-a+1)^2 - 1 }{12}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"--------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to automatically create a Discrete Uniform Distribution using Scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The mean is 3.5\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Imports\\n\",\n \"from scipy.stats import randint\\n\",\n \"\\n\",\n \"#Set up a low and high boundary for dice roll ( go to 7 since index starts at 0)\\n\",\n \"low,high = 1,7\\n\",\n \"\\n\",\n \"# Get mean and variance\\n\",\n \"mean,var = randint.stats(low,high)\\n\",\n \"\\n\",\n \"print('The mean is %2.1f' % mean)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 26,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Now we can make a simple bar plot\\n\",\n \"plt.bar(roll_options,randint.pmf(roll_options,low,high))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#####That's basically it for a discrete uniform distribution, check out the rest of the reading below if you're still interested.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"---------------------------------------------\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Example of real world use: German Tank Problem\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So now that we know some information about the uniform discrete distribution function, how about we use it to solve a problem?\\n\",\n \"\\n\",\n \"In this case we'll solve the famous German Tank Problem.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For background, first read the wikipedia page: http://en.wikipedia.org/wiki/German_tank_problem\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Excerpt from Wikipedia:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\\"In the statistical theory of estimation, the problem of estimating the maximum of a discrete uniform distribution from sampling without replacement is known in English as the German tank problem, due to its application in World War II to the estimation of the number of German tanks. Estimating the population maximum based on a single sample yields divergent results, while the estimation based on multiple samples is an instructive practical estimation question whose answer is simple but not obvious.\\\"\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"After reading the Wikipedia article, check out the following code for an example Python workout of the example problem.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Using a Minimum-variance unbiased estimator we obtain the population max is equal to :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$ Population\\\\max = sample \\\\max + \\\\frac{sample \\\\max}{sample \\\\ size} -1 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we for instance captured 5 tanks with the serial numbers 3,7,11,16 then we know the max observed serial number was m=16.\\n\",\n \"This is our sample max with a sample size of 5 tanks. Plugging into the MVUE results in:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 38,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"18.2\"\n ]\n },\n \"execution_count\": 38,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"tank_estimate = 16 + (16/5) - 1\\n\",\n \"tank_estimate\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For a Bayseian Approach:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 41,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"20.0\"\n ]\n },\n \"execution_count\": 41,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"m=16\\n\",\n \"k=5\\n\",\n \"tank_b_estimate = (m-1)*( (k-1)/ ( k-2) )\\n\",\n \"tank_b_estimate\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Remember, this is still missing the STD\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Exponential Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"####Let's learn the exponential distribution!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Frequentist A-B Testing.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Gamma Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"####Let's learn gamma distribution!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Hypothesis Testing and Confidence Intervals.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Hypothesis Testing\\n\",\n \"\\n\",\n \"Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. \\n\",\n \"\\n\",\n \"Hypothesis Testing can be broken into 10 basic steps.\\n\",\n \"\\n\",\n \" 1.) Data Testing\\n\",\n \" 2.) Assumptions\\n\",\n \" 3.) Hypothesis\\n\",\n \" 4.) Test Statistic\\n\",\n \" 5.) Distribution of Test Statistic\\n\",\n \" 6.) Decision Rule\\n\",\n \" 7.) Calculation of Test Statistic\\n\",\n \" 8.) Statistical Decision\\n\",\n \" 9.) Conclusion\\n\",\n \" 10.) p-values\\n\",\n \" \\n\",\n \"It is important to note that the initial steps can be done in different orders or at the same time, specifically, I would suggest you come up with you research question first, before going out to do data testing. Moving along:\\n\",\n \"\\n\",\n \"Let's now break down these steps:\\n\",\n \"\\n\",\n \"##### Step 1: Data Testing\\n\",\n \"\\n\",\n \"This one is pretty simple, to do any sort of statistical testing, we'll need some data from a population.\\n\",\n \"\\n\",\n \"##### Step 2: Assumptions\\n\",\n \"\\n\",\n \"We will need to make some assumptions regarding our data, such as assuming the data is normally distributed, or what the Standard Deviation of the data is. Another example would be whether to use a T-Distribution or a Normal Distribution.\\n\",\n \"\\n\",\n \"##### Step 3: Hypothesis\\n\",\n \"\\n\",\n \"In our Hypothesis Testing, we will have two Hypothesis: *The Null Hypothesis* (denoted as Ho) and the *Alternative Hypothesis* (denoted as HA). The Null Hypothesis is the hypothesis we are looking to test against the alternative hypothesis. Let's get an example of what this looks like:\\n\",\n \"\\n\",\n \"Let's assume we have a data set regarding ages of customers to a restaurant. Let's say for this particular data set we want to try to prove that the mean of that sample population is *not* 30. So we set our null hypothesis as:\\n\",\n \"\\n\",\n \"$$ H_o : \\\\mu = 30 $$\\n\",\n \"And our Alternative Hypothesis as:\\n\",\n \"$$ H_A : \\\\mu \\\\neq 30 $$ \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We could have also set out Alternative Hypothesis to be that the mean is greater than 30 or another Alternative Hypothesis we could have proposed is the mean is less than 30. We will discuss these other options later when we go into one-tail versus two-tail tests.\\n\",\n \"\\n\",\n \"Continuing on with our steps:\\n\",\n \"\\n\",\n \"##### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"Based on our assumptions, we'll choose a suitable test statistic. For example, if we believe to have a normal distribution with our data we would choose a z-score as our standard error:\\n\",\n \"\\n\",\n \"$$ z = \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}}$$\\n\",\n \"\\n\",\n \"Or if we assume to have a t-distribution we would choose a t-score (estimated standard error):\\n\",\n \"\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"\\n\",\n \"Then our test statistic is defined as:\\n\",\n \"\\n\",\n \"$$ Test \\\\ Statistic = \\\\frac{Relevant \\\\ Statistic - Hypothesized \\\\ Parameter}{ Standard \\\\ Error \\\\ of \\\\ Releveant \\\\ Statistic}$$\\n\",\n \"\\n\",\n \"\\n\",\n \"##### Step 5: Distribution of Test Statistic\\n\",\n \"\\n\",\n \"As discussed earlier, verify that whether your data should use a t or z distribution.\\n\",\n \"\\n\",\n \"##### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"Considering the distribution, we need to establish a significance level, usually denoted as alpha, α. Alpha is the probability of having a Null Hypothesis that is true, but our data shows is wrong. So alpha is the probability of rejecting a *true* Null Hypothesis. By convention, alpha is usually equal to 0.05 or 5%. This means that 5% of the time, we will falsely reject a true null hypothesis, this is best explained through a picture.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 11,\n \"metadata\": {\n \"image/jpeg\": {\n \"height\": 400,\n \"width\": 600\n }\n },\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import Image\\n\",\n \"url = 'http://images.flatworldknowledge.com/shafer/shafer-fig08_004.jpg'\\n\",\n \"Image(url,height=400,width=600)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The above image shows three types of tests. It shows 2 types of One-Tail Tests on top, and a Two-Tail Test on the bottom. You apply your significance level to a region depending on your Alternative Hypothesis (shown above each distribution).\\n\",\n \"\\n\",\n \"Let's look at the bottom two-tail test. With an alpha=0.05, then whenever we take a sample and get our test statistic (the t or z score) then we check where it falls in our distribution. If the Null Hypothesis is True, then 95% of the time it would land inbetween the α/2 markers. So if our test statistic lands inbetween the alpha markers (for a two tail test inbetween α/2, for a one tail test either below or above the α marker depending on the Alternative Hypothesis) we accept (or don't reject) the Null Hypothesis. If it landsoutside of this zone, we reject the Hypothesis.\\n\",\n \"\\n\",\n \"Now let's say we actually made a mistake, and rejected a Null Hypothesis that unknown to us was True, then we made what is called a Type I error. If we accepted a Null Hypothesis that was actually False, we've made a Type II error. Below is a handy chart depicting the error types.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/jpeg\": 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\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 16,\n \"metadata\": {\n \"image/jpeg\": {\n \"height\": 200,\n \"width\": 300\n }\n },\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# url='http://www.personal.ceu.hu/students/08/Olga_Etchevskaia/images/errors.jpg'\\n\",\n \"url='https://dfrieds.com/images/errors.jpg'\\n\",\n \"Image(url,height=200,width=300)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##### Step 7: Calculate the Test Statistic\\n\",\n \"Now that we understand our decision rule we can calculate our t or z score.\\n\",\n \"\\n\",\n \"##### Step 8: Statistical Decision\\n\",\n \"\\n\",\n \"We take what we understand from Step 6 and see where our test statistic from Step 7 lies.\\n\",\n \"\\n\",\n \"##### Step 9: Conclusion\\n\",\n \"\\n\",\n \"We check our statistical decision and conclude whether or not to reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"##### Step 10: Calculate a p-value\\n\",\n \"\\n\",\n \"The [P value](http://en.wikipedia.org/wiki/P-value) is the estimated probability of rejecting the null hypothesis of a study question when that null hypothesis is actually true. In other words, the P-value may be considered the probability of finding the observed, or more extreme, results when the null hypothesis is true – the definition of ‘extreme’ depends on how the hypothesis is being tested.\\n\",\n \"\\n\",\n \"It is very important to note: Since the p-value is used in Frequentist inference (and not Bayesian inference), it does not in itself support reasoning about the probabilities of hypotheses, but only as a tool for deciding whether to reject the null hypothesis in favor of the alternative hypothesis.\\n\",\n \"\\n\",\n \"Let's now go over an example to go through all the steps!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Example Problem 1\\n\",\n \"\\n\",\n \"There are two main types of single-sample hypothesis tests:\\n\",\n \"\\n\",\n \" 1.) When the population standard deviation σ is known or given.\\n\",\n \" 2.) When the population standard deviation σ is NOT known, and therefore we have to estimate \\n\",\n \" with s, the sample standard deviation.\\n\",\n \"\\n\",\n \"For Case 1, we use a normal (Z) distribution, for Case 2, we use the T-distribution.\\n\",\n \"\\n\",\n \"Let's start with an example. We are hired by a fast food chain to figure out the mean age of customers. The current CEO believes the mean age is 30, however we don't believe that to be True. So we now have our Null and Alternative Hypotheses:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"It is important to remember that the Null and Alternative Hypotheses must account for all possible outcomes. \\n\",\n \"\\n\",\n \"So now we will see if we can reject the Null Hypothesis in order to accept our Alternative Hypothesis. \\n\",\n \"\\n\",\n \"#### Step 1: Data\\n\",\n \"\\n\",\n \"So we take a random sample of customers and come up with the following data. From our *sample population*, we get a mean age of 27 years from a sample of 10 customers. Note: This is a sample population of the total population (referred to as just the population).\\n\",\n \"\\n\",\n \"#### Step 2: Assumptions\\n\",\n \"We will begin and get some assumptions. Based on some textbook sources you check, you assume that the population follows a normal distribution (Note: There are [specific tests](http://en.wikipedia.org/wiki/Normality_test) to check this). We also see in this textbook that given the population we could assume a variance of 20, so a standard deviation of:\\n\",\n \"\\n\",\n \"$$ \\\\sigma = \\\\sqrt{20}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"It's important to note that in a real world case it is unlikely to know the population variance, and we will discuss that in the next example. Usually you will only know your sample population's standard deviation (not the *entire* population's standard deviation).Given that we know the standard deviation, we can use a Z Distribution.\\n\",\n \"\\n\",\n \"#### Step 3: Hypothesis\\n\",\n \"\\n\",\n \"We already have our Hypotheses from above:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\\n\",\n \"\\n\",\n \"#### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"Since we have the standard deviation, we can use the Z-Statistic:\\n\",\n \"$$ z = \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}}$$\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Step 5: Distribution\\n\",\n \"\\n\",\n \"Again we have chosen the Z-Distribution, having a mean and max at zero.\\n\",\n \"\\n\",\n \"#### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"We will set our significance level (alpha) at 5%. Meaning we are trying to minimize our Type I error. So we are trying to make sure we can reject the Null Hyopthesis and minimize the chance that it was actually True. By choosing 5% we will have a certainty of 95% that we are correct if we reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 7: Calculation of Test Statistic\\n\",\n \"\\n\",\n \"Let's go ahead and calculate our Test Statistic:\\n\",\n \"$$ z= \\\\frac{\\\\overline{x}-\\\\mu_o}{\\\\sigma / \\\\sqrt{n}} = \\\\frac{27 - 30}{\\\\sqrt{20} / \\\\sqrt{10}} = -2.12 $$\\n\",\n \"\\n\",\n \"#### Step 8: Conclusion\\n\",\n \"\\n\",\n \"In order to accept or reject the Null Hypothesis we need to see where our Z score lands. If we take alpha to be 95% then we know from a [Z-Score Table](http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf) that we have to lie above 1.96 or below -1.96 as seen in the figure below:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/gif\": \"R0lGODlhqAHOAPcAAAAAAAAAgACAAACAgIAAAIAAgICAAMDAwMDcwPDKpgAAAAAAMwAAZgAAmQAAzAEA/wAzAAAzMwAzZgAzmQAzzAAz/wBmAABmMwBmZgBmmQBmzABm/wCZAACZMwCZZgCZmQCZzACZ/wDMAADMMwDMZgDMmQDMzADM/wH/AAD/MwD/ZgD/mQD/zAH//zMAADMAMzMAZjMAmTMAzDMA/zMzADMzMzMzZjMzmTMzzDMz/zNmADNmMzNmZjNmmTNmzDNm/zOZADOZMzOZZjOZmTOZzDOZ/zPMADPMMzPMZjPMmTPMzDPM/zP/ADP/MzP/ZjP/mTP/zDP//2YAAGYAM2YAZmYAmWYAzGYA/2YzAGYzM2YzZmYzmWYzzGYz/2ZmAGZmM2ZmZmZmmWZmzGZm/2aZAGaZM2aZZmaZmWaZzGaZ/2bMAGbMM2bMZmbMmWbMzGbM/2b/AGb/M2b/Zmb/mWb/zGb//5kAAJkAM5kAZpkAmZkAzJkA/5kzAJkzM5kzZpkzmZkzzJkz/5lmAJlmM5lmZplmmZlmzJlm/5mZAJmZM5mZZpmZmZmZzJmZ/5nMAJnMM5nMZpnMmZnMzJnM/5n/AJn/M5n/Zpn/mZn/zJn//8wAAMwAM8wAZswAmcwAzMwA/8wzAMwzM8wzZswzmcwzzMwz/8xmAMxmM8xmZsxmmcxmzMxm/8yZAMyZM8yZZsyZmcyZzMyZ/8zMAMzMM8zMZszMmczMzMzM/8z/AMz/M8z/Zsz/mcz/zMz//wAAAP8AM/8AZv8Amf8AzAEA//8zAP8zM/8zZv8zmf8zzP8z//9mAP9mM/9mZv9mmf9mzP9m//+ZAP+ZM/+ZZv+Zmf+ZzP+Z///MAP/MM//MZv/Mmf/MzP/M/wH/AP//M///Zv//mf//zAH//wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPD7/6SgoICAgAAA/wD/AAD///8AAP8A////AP///ywAAAAAqAHOAAAI/wD/CRxIsKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bNmzhz6tzJs6fPn0CDCh1KtKjRo0iTKl3KtKnTp1CjSp1KtarVq1izat3KtavXr2DDih1LtqzZs2jTql3Ltq3bt3Djyp1Lt67du3jz6t3L9x+Av4AFAig5eGHhiYddJr64GLHExn2tBm4M2WNiyJUbZka5OWJnzY8jf6Ws8rPnpqYNhxbdlXTKwn8zpv45O2FtwaxbGzwceGBv2715D4YNeDHl335/dy7u2/fl2AWZHzSOfDdy4dShE5S+Xbtz77mxkv+Gzhs3Qu2wk/td33x39/bs428ujzs2fePwo783jFl9fPn6mdcefgKGJ55125kHXoIIMlhgfv3Bl9llzrnnX4GV0ZdchBtWKKGD/1F4YYgGauVac9xNd56FDwo4n3L8oWfdgoJV9yF7Eab3YHYaulgdgSVedWJ9oDE4pIg94qjhhEuy2OB/DsI4440S3hddkjveFuRRQ64nopM4OtnkjiFiiSGWXz634nSfyWjkfhT2qCORW0oG5nD5XUklhBh6GKZ6ZioJYIAkArqmfBn6CaWO9ik455jk1WknoY4ud52Y4D2HnptQfrenp90FqmmMd9Z4n3ejgtqnpKy26uqrsMb/KuustNZq66245qrrrrz26uuvwAYr7LDEFmvsscgmq+yyzDbr7LPQRivttNRWay2xWl6rLUvZbuvtSd1+K65I4Y5rbkflnqsuRumu665j78ZLmLz0klvvvZbhq69G7e6rb7/+3gtwwPQOTHC8Bh/sbsIKf1scjQ0HfN3DEEe8MMRdWrxuxS2OqPG4HOe538fehgwimyRre5tpJqeMrJazMezyrNnWJvPMr3a7Ms7Lhgszzy9bVDPQxaarM9HCtusz0r/2W+7NTOcFsNFR6zo1u1XfOrDTWdNq8NVdw5rw1mG7yvDXQFPcacczQU2SzGg/pXaiObnNbqMni0yT3fbm/8sR35zhrffabfsEZJA3ny03pZEdbiDUijvleF9ABnelydwJF+rldH8HeEWQf/Q5Z4RaHmqbUo74o40tpggTfpGW6VCTgs85KKY8uQ235PrFrmaRANa+KuHU3VT8gFVOGKVrnBKfPE66gzS6Sccr+PyhiFrYfOeITq/ayY9ar1DmM2LG+qC2F96330s5Hv6fwDVvqvkYv0n4Su77GOiFaJ4nqqrem91IQtc+xj1KfiPrH8rYlqr7lcaADOQeApE0MsYpSiZ8I6BS8kc8CSpQfDXCnp4wCMHbVYw4t6MSCjunuZoALnobLOGSlGeo1t1IcJRqIQnBdyZLjelym2NgEP9t8sL1IYWDDfTfD4fYISEy0Vyfs1sAywaVKA6QingZXQaxWJfpFZGLcfHeF8H4FjFSj4xuCaAW0cgWNYKLjWqZohcV9rDxuc50ZJHja4ZSRztOLH15rKCpbEOnQOJvj0H5HRBV5KW0ZGw5NTTkAxFpODCxrT54QssjSeXArUzxkiH5JEUy5kA8toV5rhucV0Spx6LkKJWdzGN/FJm30SjmkHxMFC1BKckn6U2U0LslLoHyIksC03A/syBDKNZHoxzzk8f0zNBqaZZpGqll/HHmS1hJm1EG6Hy2/F4tMzk1K24kmtzsCcuMCb+xbPKC4ovbFc/5OmHqhJS7/FM0icj/zOTVr4l/exs969mSfcaomd2jEXEMahcp8muHBYVjQEP50Jg8U6ITFZ1s1GdPjGJNo4zZG0E9ulH2gU6kIyWp0EB6UpSmVKXeRFdIXbpNmM40o/CiaU1tGlOcnoaIOmUKQ3Mztp66MKgFtFZRc3pUpB5RZTJdjfGaKtRtLRUiQ7XkS52Z1cf5dJk76Wosw4rNZ8kTeHWDnlg3dJy1Iu6rhMzdPV2oKXCWDK4iDOZcLepWW8FSquIMq1wV01eaSYdrYK3kYAM7UIKlB2zAISYyGVvSgz22oguULG1oiNd/eWylvtQsMTmE2YbZ9afwFG0iJwdai5UVeK/VK1EQiJjT/+4LbbFNK5cyGdLh2DZrv+1mUoI7vhRyEaHDLWBu9bRckh12rKrd7SBrW9hmpQiQXGpfeYgbwrJNpnSoSeqi/updtZEpta5M6uGYWV1smZd/gmwvVpWbQyWS91/v/VKhVBXDDa5XmfND7l3Ziyo5gYhA8n1IghPbXY/p98H97BmBU7ffCuvXuE/tb4X5p8MNL1TAXpuwn2j5YEVBGL3p7e+FSzxiRSJpwguuG4zza2A+LS9K9c1Tc3Wb3BUf+MdAHh6HZ8zdthH5yEhOspKXzOQmO/nJUI6ylKdM5Spb+coExlWMGZxhnlZWw1328k3BnF0xf1S8YTazUZNLZjUDlv/NcHYzU+NcZjnPWWt2zrOe98znPvv5z4AOtKAHDS0mgfO+3LItoiNq3wwVOWoYu7CQtylpE/PTf3mr9HHXlinWQnRwpIyo+UbISzaStsHQHeY4GYnU46gSo6dWnec+/UtWczTTM9xx2jIrPB9t1Ya2pnWD8TbD416KTZxKHzrzyj1hzw95i/JozFCkVUquuto7LRJvX03F1OQz1RTVaqwtKkBUc9u7oc0UtkkH4FBvtdOZJilpFYri13SY1LqeZw5PlG+epcmujx4gLLHT7/XVNX6ETrjCF87whjv84RCPuMQnTvGKW/ziGM+4xjfO8Y57/OMgD7nIR07ykpv85CgKT7nKV87yloMlIAA7Ow==\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 27,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url='https://www.sfu.ca/personal/archives/richards/Zen/Media/Ch17-9.gif'\\n\",\n \"Image(url)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Given that our Z-score for our Test Statistic was -2.12, we can see that we can reject the Null Hypothesis! So we reject that the mean of the customer age is 30. Remember, this test does not actually tell us what the mean is, only that it unlikely to be 30. How unlikely? This is where the p-value comes into play.\\n\",\n \"\\n\",\n \"#### Step 9: p-value\\n\",\n \"\\n\",\n \"From a table, we can see that 98.3% corresponds to the percentage of the area inbetween our +/- of our Z-Score, 2.12. This means that if the reality is the Null Hypothesis is actually True, we would only find that data 100-98.3= 1.7% of the time. So our p-value is 1.7% (or 0.017). This is pretty unlikely so we can be quite confident in our rejection of the Null Hypothesis.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Confidence Intervals\\n\",\n \"\\n\",\n \"We could describe the above process using confidence intervals. The equation for a confidence interval is:\\n\",\n \"$$ \\\\bar{x} \\\\pm z \\\\sigma _\\\\bar{x} $$\\n\",\n \"\\n\",\n \"From our work above we can fill in the equation as:\\n\",\n \"$$ 27 \\\\pm 1.96 *(\\\\frac{\\\\sqrt{20}}{\\\\sqrt{10}}) $$\\n\",\n \"\\n\",\n \"Which (with rounding) is equal to:\\n\",\n \"$$ 27 \\\\pm 2.77 $$\\n\",\n \"\\n\",\n \"This gives us a range between 24.23 and 29.77. Since the Null Hypothesis mean of 30 is NOT in that range, we can reject that Null Hypothesis. A simple approach to the above problem!\\n\",\n \"\\n\",\n \"Now what is we don't know the standard deviation? Let's go ahead and look at an example problem:\\n\",\n \"\\n\",\n \"### Example Problem 2\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Assuming the same problem as before, we want to know whether or not we can reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 1: Data\\n\",\n \"\\n\",\n \"Let's say after getting our data, we have a mean of 27 form 10 customers. Our *sample population* has a standard deviation of 3.\\n\",\n \"\\n\",\n \"#### Step 2: Assumptions\\n\",\n \"\\n\",\n \"In this second case we don't consult a textbook so we don't know what the entire populations standard deviation is.\\n\",\n \"\\n\",\n \"\\n\",\n \"#### Step 3: Hypotheses\\n\",\n \"\\n\",\n \"Same as before:\\n\",\n \"$$ H_o: \\\\mu = 30 $$\\n\",\n \"$$ H_A: \\\\mu \\\\neq 30 $$\\n\",\n \"\\n\",\n \"#### Step 4: Test Statistic\\n\",\n \"\\n\",\n \"We now have to use the t-distribution since we don't know the populations standard deviation. So our test statistic will be:\\n\",\n \"\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"#### Step 5: Distribution\\n\",\n \"\\n\",\n \"Since we only have 10 customers in our sample and don't know the entire population's standard deviation we use a t-distribution. Remember as a sample population grows beyond 30, the t distribution begins to resemble and behave like a standard Z distribution. Keep in mind a t-distribution is \\\"flatter\\\" and operates on degrees of freedom (n-1).\\n\",\n \"\\n\",\n \"We can use a [T-table](http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf) to find that for a 95% significance level, our region for accepting the Null Hypothesis falss between +/- 2.262\\n\",\n \"\\n\",\n \"#### Step 6: Decision Rule\\n\",\n \"\\n\",\n \"As before: We will set our significance level (alpha) at 5%. Meaning we are trying to minimize our Type I error. So we are trying to make sure we can reject the Null Hyopthesis and minimize the chance that it was actually True. By choosing 5% we will have a certainty of 95% that we are correct if we reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 7: Calculate our Test Statistic\\n\",\n \"\\n\",\n \"Plugging into:\\n\",\n \"$$ t = \\\\frac{\\\\overline{x}-\\\\mu_o}{s/ \\\\sqrt{n}}$$\\n\",\n \"we get:\\n\",\n \"$$ t = \\\\frac{27-30}{3/ \\\\sqrt{10}}=-3.16$$\\n\",\n \"\\n\",\n \"#### Step 8: Statisitcal Decision\\n\",\n \"\\n\",\n \"Given the rejection regions was t = +/- 2.262 , then our t=-3.16 allows us to reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"#### Step 9: Conclusion\\n\",\n \"\\n\",\n \"Just as before we can reject the Null Hypothesis.\\n\",\n \"\\n\",\n \"\\n\",\n \"### Additional Resources\\n\",\n \"\\n\",\n \"Here are some more great resources for learning about Hypothesis Testing:\\n\",\n \"\\n\",\n \"1.) [Wolfram](http://mathworld.wolfram.com/HypothesisTesting.html)\\n\",\n \"2.) [Stat Trek](http://stattrek.com/hypothesis-test/hypothesis-testing.aspx)\\n\",\n \"3.) [Wikipedia](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing)\\n\",\n \"4.) [Probability Book Sample](http://www.sagepub.com/upm-data/40007_Chapter8.pdf)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Kolmogorov-Smirnov Test.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Markov Chain Monte Carlo Algorithm.ipynb", "content": "{\n \"cells\": [],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Normal Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"#### Let's learn the normal distribution! Note: You should check out the binomial distribution first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We'll start with the definition of the PDF, we'll see how to create the distribution in python using scipy and numpy, and discuss some properties of the normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The distribution is defined by the probability density function equation:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## $$ f(x,\\\\mu,\\\\sigma) = \\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}e^\\\\frac{-1}{2z^2} $$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where: $$z=\\\\frac{(X-\\\\mu)}{\\\\sigma}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"where: μ=mean , σ=standard deviation , π=3.14... , e=2.718... The total area bounded by curve of the probability density function equation and the X axis is 1; thus the area under the curve between two ordinates X=a and X=b, where a\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"from IPython.display import Image\\n\",\n \"Image(url='http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/The_Normal_Distribution.svg/725px-The_Normal_Distribution.svg.png')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's learn how to use scipy to create a normal distribution\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 21,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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myBICpq6asrAybNm0CALz55puIjo5GfHw8ANO6LK+++iqeeuopyzVfeuklTJo0CUOHDoVWq8Xrr7+O4uJivPnmm7a4RyKyge3tK9vOGzPoJ7uAXYEgCLh7XCT+tPsM/v1tGe4aFyl1SURuzerAkpmZidraWqxevRoVFRVITExEbm4uYmJMO51WVFSgpOT73U6NRiNWrlyJixcvQqFQIC4uDi+//DIef/xxyzn19fV47LHHUFlZCbVajXHjxiE/Px8TJ060wS0SUV/VNemRf+YqAPfoDjK7a9wg/Gn3Gew/V4MqbQvCXWDPJCJnJYii6BJz9rRaLdRqNTQaDfz9/aUuh8il/L3gEp7ffhwjB/rjP/+VLnU5/eqedQdQePkaXrgjAb+YHCt1OUQup6ev39xLiIh+0kft3UHzx7reyrY/5Y7RprF0nxwpl7gSIvfGwEJEN1Ra14zCy9cgCMAdY9ynO8js1lEDIAjAtyX1uHKtWepyiNwWAwsR3dD2YtM6JKk3BSNC7X5jOML8VZgUa9qR+j/fcQdnIqkwsBDRDX1yxPQi7Y7dQWbmlqVPvmO3EJFUGFiIqFvnqhtxuqoBHnIBs0e674akcxIjIJcJOFamxYWrjVKXQ+SWGFiIqFs7jppaVyYPCYHa20PiaqQT5OOJKUNCAACfsluISBIMLETUrf+0B5ZbE7nqtLlb6FN2CxFJgoGFiLp04WojTlU2QCETkDHSdXdm7qmMkeHwlMtwpqoRpysbpC6HyO0wsBBRl3YcM+2fkxoXjABvT4mrkZ6/ygPThocCYCsLkRQYWIioS7nt3UG3jWJ3kNmto0wDj7kZIlH/Y2Ahok4u1zbheLkWcpmADDeeHfRjM+LD4SEXcKaqEec5W4ioXzGwEFEnuUfbu4NuCkaQD7uDzNReHkiLM80W+uwYW1mI+hMDCxF1Yu4OmjuKrSs/NieR3UJEUmBgIaIOSuuacbRMA5kAt14srjuzEsIhCMB3VzQoq78udTlEboOBhYg6MLeupMQGI8RXKXE1jifEV4kJg4MAADvZLUTUbxhYiKiDz9q7Om5ld1C35rS3PH3GbiGifsPAQkQW1doWFJXUAwBnB93A7PZxLN9cqsPVBp3E1RC5BwYWIrLYfbIaADAmKgDh/iqJq3FcgwK8MDpSDVEEdp+skrocIrfAwEJEFnknTF0cGQlciv+nmAckc3ozUf9gYCEiAECjrg1fnasFwMDSE+bpzQfO10BzvVXiaohcHwMLEQEA8s9chd5gxOBgbwwJ85W6HIcXF+qLYeG+aDWI+OIUu4WI7I2BhYgAAHknTC+6GSMjIAiCxNU4h4wEUyvL7hPVEldC5PoYWIgIrQYjPm8fPDqL3UE9NnNEGABg75mr0LcZJa6GyLUxsBARvrlYB21LG4J9PDE+OlDqcpzGmMgAhPgq0ahrw6GLdVKXQ+TSGFiICLvau4NmjgiDXMbuoJ6SyQTMjDe1snB6M5F9MbAQuTlRFC3jV2YlcLE4a5m7hXafrIIoihJXQ+S6GFiI3NyJCi3K6q/Dy0OO9KEhUpfjdKYMDYFSIcOVa9dxuqpB6nKIXBYDC5GbM7eupA8NgcpDLnE1zsfbU4HJQ0xB7/OTnC1EZC8MLERuzvwiewtnB/XaLSNM/3ccx0JkPwwsRG6sWtuCo2UaCAIwfXiY1OU4LfM4luLSem6GSGQnDCxEbuzL06bWldGRAQj1U0pcjfMK91dh1CDTZohfnmK3EJE99CqwrF27FrGxsVCpVEhKSsK+ffu6PXf//v2YPHkygoOD4eXlhfj4ePzpT3/qdN7WrVuRkJAApVKJhIQEbNu2rTelEZEVvmh/cZ3B1pU+M3cL5bFbiMgurA4sOTk5WL58OVatWoWioiKkp6dj7ty5KCkp6fJ8Hx8fPPnkk8jPz8fJkyfx3HPP4bnnnsOGDRss5xQUFCAzMxNZWVk4cuQIsrKycN999+HgwYO9vzMiuiFdmwH7ztYA+L5Lg3rP/H+4/2wNWloNEldD5HoE0cqFA1JSUjB+/HisW7fOcmzEiBGYP38+srOze3SNu+++Gz4+Pvj73/8OAMjMzIRWq8WOHTss58yZMweBgYHYvHlzj66p1WqhVquh0Wjg7+9vxR0Ruad9Z68i651DCPNT4uCvZ3L/oD4SRRFpL3+BCk0L3n04GTPiOYiZqCd6+vptVQuLXq9HYWEhMjIyOhzPyMjAgQMHenSNoqIiHDhwANOmTbMcKygo6HTN2bNn3/CaOp0OWq22w4OIes7cHTR9eBjDig0IgvCDReQ4joXI1qwKLDU1NTAYDAgP7/iXQ3h4OCorK2/43MjISCiVSiQnJ2Pp0qVYvHix5WOVlZVWXzM7OxtqtdryiIqKsuZWiNyaKIrfj19hd5DNzGwfx/I5V70lsrleDbr98V9joij+5F9o+/btw+HDh/HWW29hzZo1nbp6rL3mypUrodFoLI/S0lIr74LIfV2oacLl2mZ4ymWYMoSr29pK6k3B8PKQo0qrw8kKrnpLZEsKa04OCQmBXC7v1PJRXV3dqYXkx2JjYwEAo0aNQlVVFV588UU88MADAICIiAirr6lUKqFUchomUW+Yp96m3BQEH6VVvwboBlQecqTFBePzU9X48nQ1EgZyPB2RrVjVwuLp6YmkpCTk5eV1OJ6Xl4e0tLQeX0cUReh03y+ulJqa2umau3btsuqaRNRz5tVtZ8SzO8jWbm7/P91zmuNYiGzJ6j+tVqxYgaysLCQnJyM1NRUbNmxASUkJlixZAsDUVVNWVoZNmzYBAN58801ER0cjPj4egGldlldffRVPPfWU5ZrLli3D1KlT8corr2DevHnYvn07du/ejf3799viHonoB7QtrfjmUh0ABhZ7uHlYKACg8PI1aJpbofb2kLgiItdgdWDJzMxEbW0tVq9ejYqKCiQmJiI3NxcxMTEAgIqKig5rshiNRqxcuRIXL16EQqFAXFwcXn75ZTz++OOWc9LS0rBlyxY899xzeP755xEXF4ecnBykpKTY4BaJ6If2n61Bm1HETaE+iAn2kboclxMV5I2hYb44W92I/LNXcceYgVKXROQSrF6HxVFxHRainvnvD45g67dX8Gh6LFbdliB1OS7pD7knsSH/Au4ZH4k/3jdG6nKIHJpd1mEhIudmNIrYe6Z9/RV2B9nNzcNN3UJ7z1TDaHSJvwmJJMfAQuRGvivToKZRDz+lAhMGB0ldjstKjgmCr1KBmkY9jpVrpC6HyCUwsBC5kS/aN+abOiwUHnL++NuLp+L79W2+PHVV4mqIXAN/YxG5kS9Pm1482R1kf9PjTd1CX3J6M5FNMLAQuYmaRh2Olpm6J6YO4+q29jZtmCkUHrlSj9pG3U+cTUQ/hYGFyE3sO2tqXRk50B9hfiqJq3F9EWoVRgzwhygC+WfZLUTUVwwsRG5ib3t30LT2hc3I/qa3zxbiOBaivmNgIXIDRqOI/LM1ABhY+pN5rFD+2aswcHozUZ8wsBC5gWPlGtQ16eGrVGB8TKDU5biNcVEB8FcpUN/ciuLSeqnLIXJqDCxEbsDcHTR5SDCnM/cjhVyGqe0tWtwMkahv+JuLyA3sPWMKLDcP53Tm/ja9/f+c05uJ+oaBhcjFaZpb8W3JNQCw/LVP/Wda+8DbY2VaVDe0SFwNkfNiYCFycV+dr4FRBIaG+WJQgJfU5bidEF8lEgeZNnTbd6ZG4mqInBcDC5GL43Rm6Zn/77keC1HvMbAQuTBRFC3jV8xdE9T/pg41/d/vO1vD3ZuJeomBhciFna5qQKW2BSoPGXdnltD4mED4KhWoa+LuzUS9xcBC5MLM3UGpNwVD5SGXuBr35SGXIS0uGMD3XxMisg4DC5ELs3QHcfyK5MxdchzHQtQ7DCxELqpJ14ZvLtUBAKZx/RXJmcexfFtSD21Lq8TVEDkfBhYiF1VwvhatBhHRQd4YHOwtdTluLyrIGzeF+sBgFHHgHKc3E1mLgYXIRf2wO0gQBImrIeD7Vpa9XI+FyGoMLEQuSBRF7DljWgqe41cch2Ucy5mrEEVObyayBgMLkQu6VNuM0rrr8JTLkNo+O4WkNyk2GJ4KGcrqr+P81SapyyFyKgwsRC5ob/tGexNiA+GjVEhcDZl5ecoxsX09HHOXHRH1DAMLkQvidGbHZVmmn4GFyCoMLEQupqXVgIILtQCAacM4ndnRmHfM/vpCLVpaDRJXQ+Q8GFiIXMw3l+rQ0mpEhL8Kw8J9pS6HfmRYuC8i/FXQtRlx6GKd1OUQOQ0GFiIX88PdmTmd2fEIgoCpw0IAcBwLkTUYWIhczB7uzuzwzF11HMdC1HMMLEQu5Mq1ZpyrboRcJmDykBCpy6FuTBkSApkAnK1uRHn9danLIXIKDCxELiS/fQXVcVEBUHt5SFwNdUft7YGxUQEA2MpC1FO9Cixr165FbGwsVCoVkpKSsG/fvm7P/fe//41Zs2YhNDQU/v7+SE1Nxc6dOzucs3HjRgiC0OnR0tLSm/KI3Nbe9tVtp3I6s8Mzf424ezNRz1gdWHJycrB8+XKsWrUKRUVFSE9Px9y5c1FSUtLl+fn5+Zg1axZyc3NRWFiI6dOn44477kBRUVGH8/z9/VFRUdHhoVKpendXRG6o1WDEgXPm6cwMLI7O/DXad7YGbQajxNUQOT6rl8B87bXXsGjRIixevBgAsGbNGuzcuRPr1q1DdnZ2p/PXrFnT4f0//OEP2L59Oz755BOMGzfOclwQBERERFhbDhG1Ky6tR4OuDYHeHkgcpJa6HPoJoyMDEODtgfrmVhy5Uo+kmCCpSyJyaFa1sOj1ehQWFiIjI6PD8YyMDBw4cKBH1zAajWhoaEBQUMcfzsbGRsTExCAyMhK33357pxaYH9PpdNBqtR0eRO7MPBYifWgo5DJOZ3Z0PxwYbZ6KTkTdsyqw1NTUwGAwIDw8vMPx8PBwVFZW9ugaf/zjH9HU1IT77rvPciw+Ph4bN27Exx9/jM2bN0OlUmHy5Mk4e/Zst9fJzs6GWq22PKKioqy5FSKXY17Tg+NXnIe5W2jv2RqJKyFyfL0adPvjxahEUezRAlWbN2/Giy++iJycHISFfb9k+KRJk7BgwQKMGTMG6enp+OCDDzBs2DC88cYb3V5r5cqV0Gg0lkdpaWlvboXIJdQ16XG0TAMAmDqU05mdxdShpsDy3ZV61DXpJa6GyLFZFVhCQkIgl8s7taZUV1d3anX5sZycHCxatAgffPABbrnllhsXJZNhwoQJN2xhUSqV8Pf37/Agclf7zl6FKALxEX4I8+dgdWcRoVYhPsIPogjsP8dWFqIbsSqweHp6IikpCXl5eR2O5+XlIS0trdvnbd68GQ8//DDef/993HbbbT/5eURRRHFxMQYMGGBNeURuy7z+CmcHOR9zFx7HsRDdmNWzhFasWIGsrCwkJycjNTUVGzZsQElJCZYsWQLA1FVTVlaGTZs2ATCFlYULF+LPf/4zJk2aZGmd8fLyglptmsnw0ksvYdKkSRg6dCi0Wi1ef/11FBcX480337TVfRK5LFEUse8sx684q2nDQrEh/wLyz17tcfc6kTuyOrBkZmaitrYWq1evRkVFBRITE5Gbm4uYmBgAQEVFRYc1WdavX4+2tjYsXboUS5cutRx/6KGHsHHjRgBAfX09HnvsMVRWVkKtVmPcuHHIz8/HxIkT+3h7RK7vVGUDqht08PKQI3lwoNTlkJWSBwfCy0OOqw06nKxoQMJAdm8TdUUQRVGUughb0Gq1UKvV0Gg0HM9CbuWtvefx8o5TmBEfhncfniB1OdQLj2z8Bl+cqsazc+OxZFqc1OUQ9auevn5zLyEiJ2def4Wzg5yX+WvHcSxE3WNgIXJizfo2HL50DQDHrzizacNNyzwcvlyHJl2bxNUQOSYGFiIn9vWFWugNRkQGeiE2xEfqcqiXBgd7IzrIG60GEQXna6Uuh8ghMbAQOTHzdOapw0I5u8SJCYKAqcNM3ULcvZmoawwsRE7MvBw/119xftOGmbqFzF9TIuqIgYXISZXWNeNiTRMUMgFpccFSl0N9lBoXDIVMwOXaZlyqaZK6HCKHw8BC5KTMf4mPjw6En8pD4mqor3yVCss6OuwWIuqMgYXISVmmMw/jdGZXwWX6ibrHwELkhFoNRhxon03C6cyuwzwWqeBCLXRtBomrIXIsDCxETqiopB6NujYE+XgicaBa6nLIRkZE+CPEV4lmvQGF7evrEJEJAwuRE9p7phoAkD40BDIZpzO7Cpns++nNezmOhagDBhYiJ2RZf2Uou4NczTSOYyHqEgMLkZOpbdThWLkGAJDOAbcuZ8qQEAiCaRfuKm2L1OUQOQwGFiIns/9cDUQRGDHAH2F+KqnLIRsL9lVi9CDTuKR8LiJHZMHAQuRk9nI6s8szz/zKP1sjcSVEjoOBhciJGI2iZfwKl+N3Xeav7b6zV2EwihJXQ+QYGFiInMjJSi1qGnXw9pQjOSZI6nLITsZGBcBPpUB9cyu+u1IvdTlEDoGBhciJmFtXUm8KhqeCP76uSiGXYcqQ9t2bz7BbiAhgYCFyKt8vx8/uIFdnWaa/fc0dInfHwELkJJp0bTh8uQ4AA4s7MH+Ni0vroWlulbgaIukxsBA5ia8v1KLVICIqyAuDg72lLofsbFCAF4aE+cIomqayE7k7BhYiJ2GezjxtWCgEgcvxuwPzbCGux0LEwELkNCzjV7gcv9uwLNN/5ipEkdObyb0xsBA5gZLaZlyqbYZCJiA1LljqcqifTIwNglIhQ6W2BWerG6Uuh0hSDCxETsC8c+/4mED4qTwkrob6i8pDjkk3mQIqN0Mkd8fAQuQE8n8wfoXcy9QfdAsRuTMGFiIHp28z4sA5Lsfvrsxf80MX69Csb5O4GiLpMLAQObjDl+rQpDcgxFeJhAH+UpdD/Swu1AeDArygNxhx8EKd1OUQSYaBhcjB7flBd5BMxunM7kYQBHYLEYGBhcjhfXnKtDT7zcPZHeSupg0z7yvEwELui4GFyIGV1V/H2epGyASuv+LO0oaEQC4TcKGmCaV1zVKXQySJXgWWtWvXIjY2FiqVCklJSdi3b1+35/773//GrFmzEBoaCn9/f6SmpmLnzp2dztu6dSsSEhKgVCqRkJCAbdu29aY0Ipey57SpdWV8dCDU3pzO7K78VR5Iig4EwG4hcl9WB5acnBwsX74cq1atQlFREdLT0zF37lyUlJR0eX5+fj5mzZqF3NxcFBYWYvr06bjjjjtQVFRkOaegoACZmZnIysrCkSNHkJWVhfvuuw8HDx7s/Z0RuYA97WtvsDuIprJbiNycIFq53nNKSgrGjx+PdevWWY6NGDEC8+fPR3Z2do+uMXLkSGRmZuI3v/kNACAzMxNarRY7duywnDNnzhwEBgZi8+bNPbqmVquFWq2GRqOBvz9nUpDz07UZMH51Hpr0Bnz61BQkDlJLXRJJ6OgVDe74y374KhUo+s0seMjZo0+uoaev31Z9x+v1ehQWFiIjI6PD8YyMDBw4cKBH1zAajWhoaEBQUJDlWEFBQadrzp49+4bX1Ol00Gq1HR5EruTwpWto0hsQ6sfpzASMHOiPYB9PNOra8O3la1KXQ9TvrAosNTU1MBgMCA8P73A8PDwclZWVPbrGH//4RzQ1NeG+++6zHKusrLT6mtnZ2VCr1ZZHVFSUFXdC5PjM41c4nZkAQCYTkD7U1C20h91C5IZ61ab4463tRVHs0Xb3mzdvxosvvoicnByEhYX16ZorV66ERqOxPEpLS624AyLHx/Er9GPT2r8X9nBfIXJDCmtODgkJgVwu79TyUV1d3amF5MdycnKwaNEifPjhh7jllls6fCwiIsLqayqVSiiVSmvKJ3IaV641W6Yzpw9hYCGTqUNDIQjAyQotKjUtiFCrpC6JqN9Y1cLi6emJpKQk5OXldTiel5eHtLS0bp+3efNmPPzww3j//fdx2223dfp4ampqp2vu2rXrhtckcmXmv6A5nZl+KNhXibFRAQCAL9u7DInchVUtLACwYsUKZGVlITk5GampqdiwYQNKSkqwZMkSAKaumrKyMmzatAmAKawsXLgQf/7znzFp0iRLS4qXlxfUatOsh2XLlmHq1Kl45ZVXMG/ePGzfvh27d+/G/v37bXWfRE7FHFimx4f9xJnkbqYPD0NRST2+PFWNByZGS10OUb+xegxLZmYm1qxZg9WrV2Ps2LHIz89Hbm4uYmJiAAAVFRUd1mRZv3492trasHTpUgwYMMDyWLZsmeWctLQ0bNmyBe+99x5Gjx6NjRs3IicnBykpKTa4RSLnomsz4MB57s5MXZvRHmL3n6uBrs0gcTVE/cfqdVgcFddhIVfx1bka/Pztgwj1U+LQr2f2aEA7uQ+jUURK9ue42qDDPxalYEr7zCEiZ2WXdViIyP7Mmx1OGxbKsEKdyGQCprfPFvriFMexkPtgYCFyMOY1NjidmbozfbipW2gPB96SG2FgIXIgV64141x1I+QygdOZqVtThoZA0b5786WaJqnLIeoXDCxEDuT76cwBnM5M3fJTeWDCYNP2JpzeTO6CgYXIgZib+G8ezunMdGPm2UIcx0LugoGFyEG0tBpw4HwtAE5npp9mXqPn4IU6NOvbJK6GyP4YWIgcxMGLdWjWGxDur8TIgZyaTzcWF+qDqCAv6A1GfHWuVupyiOyOgYXIQXx+sgoAMCM+nNOZ6ScJgoAZ7V2HHMdC7oCBhcgBiKKIz0+aXnRmcjl+6qGb279XvjxVDRdZA5SoWwwsRA7gTFUjyuqvQ6mQYfIQrlxKPZN6UzBUHjJUaFpwuqpB6nKI7IqBhcgB7G7vDpo8JARennKJqyFnofKQIy3OFHA5W4hcHQMLkQMwv9jMYHcQWWn6D7qFiFwZAwuRxGobdfi25BoAYOYIBhayjnlfocLL16BpbpW4GiL7YWAhktie01chikDCAH8MUHtJXQ45mchAbwwL94VRBPacYSsLuS4GFiKJfX7KNH7lFrauUC/NHBEOANh9koGFXBcDC5GE9G1G5J+pAQDMaH/RIbLWLe3fO3tOV0PfZpS4GiL7YGAhktChi3Vo1LUhxFeJ0YPUUpdDTmpsVABCfD3R0NKGby7VSV0OkV0wsBBJyNwdNCM+FDIZV7el3pHLBMsMs7wTVRJXQ2QfDCxEEvnh6rYz4tkdRH1zi2UcSxVXvSWXxMBCJJHzVxtRUtcMT7kM6UO5ui31TfrQUCgVMly5dp2r3pJLYmAhkoi5dWVSXDB8lAqJqyFn5+UptwTf3ewWIhfEwEIkEXNg4XRmshVzt1AepzeTC2JgIZLAtSY9Dl82zebgcvxkKzPaw++R0npUa1skrobIthhYiCTwxalqGEUgPsIPkYHeUpdDLiLMT4WxUQEAgM+5txC5GAYWIgnsPF4JAJg9MkLiSsjVzEpony3EcSzkYhhYiPrZdb0B+WevAgAyRnI6M9mWeRzL/nM1aNa3SVwNke0wsBD1s31nr6Kl1YhBAV5IGOAvdTnkYoaF+yIqyAu6NiP2n62Ruhwim2FgIepnu9qb6jNGhkMQuLot2ZYgCB0WkSNyFQwsRP2ozWDE5+0vIhkJHL9C9jGrPbB8frIaBiNXvSXXwMBC1I++uXQN15pbEeDtgQmDA6Uuh1zUhNgg+KkUqG3So6jkmtTlENkEAwtRP9p1wjQ7aGZ8OBRy/viRfXjIZZb1fXZxthC5iF79xly7di1iY2OhUqmQlJSEffv2dXtuRUUFHnzwQQwfPhwymQzLly/vdM7GjRshCEKnR0sLFz4i1yGKInYdN714zObsILKzOe1T5j87VsnNEMklWB1YcnJysHz5cqxatQpFRUVIT0/H3LlzUVJS0uX5Op0OoaGhWLVqFcaMGdPtdf39/VFRUdHhoVKprC2PyGGdqNCirP46VB4ypA8NlboccnHThodC5SFDSV0zTlRopS6HqM+sDiyvvfYaFi1ahMWLF2PEiBFYs2YNoqKisG7dui7PHzx4MP785z9j4cKFUKvV3V5XEARERER0eBC5EnPrytShofDylEtcDbk6b08Fpg0zBeOdxyolroao76wKLHq9HoWFhcjIyOhwPCMjAwcOHOhTIY2NjYiJiUFkZCRuv/12FBUV3fB8nU4HrVbb4UHkyMyr22ZwdVvqJ3MSTd9rOxhYyAVYFVhqampgMBgQHt6x/z08PByVlb3/gYiPj8fGjRvx8ccfY/PmzVCpVJg8eTLOnj3b7XOys7OhVqstj6ioqF5/fiJ7K6ltxqnKBsgEYCY3O6R+MiM+HB5yAWerG3GuulHqcoj6pFeDbn+82JUoin1aAGvSpElYsGABxowZg/T0dHzwwQcYNmwY3njjjW6fs3LlSmg0GsujtLS015+fyN7Ms4MmxgYh0MdT4mrIXai9PJAWFwLg+xY+ImdlVWAJCQmBXC7v1JpSXV3dqdWlT0XJZJgwYcINW1iUSiX8/f07PIgc1WfHuNkhScPcLfQZu4XIyVkVWDw9PZGUlIS8vLwOx/Py8pCWlmazokRRRHFxMQYMGGCzaxJJpVLTgsOXTYt3mV88iPrLrIRwyATgaJkGV641S10OUa9Z3SW0YsUKvP3223j33Xdx8uRJPP300ygpKcGSJUsAmLpqFi5c2OE5xcXFKC4uRmNjI65evYri4mKcOHHC8vGXXnoJO3fuxIULF1BcXIxFixahuLjYck0iZ/bZsQoAwPjoAAxQe0lcDbmbEF8lJgwOAsBWFnJuCmufkJmZidraWqxevRoVFRVITExEbm4uYmJiAJgWivvxmizjxo2z/LuwsBDvv/8+YmJicOnSJQBAfX09HnvsMVRWVkKtVmPcuHHIz8/HxIkT+3BrRI4ht/1F4tZRbDEkacxJjMDBi3XYebwSi9Nvkrocol4RRBdZAlGr1UKtVkOj0XA8CzmMam0LUrI/hygCXz07A4MC2MJC/a+8/jrSXv4CggAc/PVMhPlxUU5yHD19/eZmJkR2tPN4JUQRGBsVwLBCkhkY4IUxUQEQxe8XMCRyNgwsRHb0n6Om8Su3sTuIJPbDvYWInBEDC5GdXG3Q4dDFOgCcHUTSm9v+PVhwoRa1jTqJqyGyHgMLkZ3sPF4JowiMiVQjKshb6nLIzQ0O8UHiIH8YjCKX6ienxMBCZCc72qczz2V3EDmI20cPBAB8+l25xJUQWY+BhcgOaht1KDhfCwC4NZGBhRyDeSzVwYt1qNa2SFwNkXUYWIjsYNeJKhhFIHGQP6KD2R1EjiEqyBvjok2zhXLbB4QTOQsGFiI7+OSIqcmdi8WRo/m+W4iBhZwLAwuRjVVpW1BwwdQddEf7iwORo7ht1AAIAnD48jWU11+XuhyiHmNgIbKxT7+rgCgCSTGBnB1EDidCrcKEGNPeQv9hKws5EQYWIhv7uL076M4xbF0hx3T7GFNXJWcLkTNhYCGyoUs1TThSWg+ZwPEr5LjmJg6ATACOXNGgpLZZ6nKIeoSBhciGzINtJw8JQaifUuJqiLoW6qdEalwwAODTo2xlIefAwEJkI6IoYju7g8hJmGcLfVzMwELOgYGFyEZOVjTgXHUjPBUyzObeQeTg5iZGwEMu4FRlA05VaqUuh+gnMbAQ2cj2I2UAgBnDw+Cv8pC4GqIbC/D2xPThYQCAbUVlEldD9NMYWIhswGgU8ekR0xTRO8eyO4icw93jBwEAtheVw2AUJa6G6MYYWIhsoLDkGsrqr8NXqcCM+DCpyyHqkenxYfBXKVCpbcHB9sUOiRwVAwuRDXzU3qSeMTIcKg+5xNUQ9YxSIcdt7YNv/81uIXJwDCxEfdTSarBMZ757XKTE1RBZx9wttONoBa7rDRJXQ9Q9BhaiPtp9sgraljYMVKssa1sQOYuk6EBEBnqhSW/ArhOVUpdD1C0GFqI+2lp4BQBw1/hBkMsEiashso5MJuCucaZWlo/YLUQOjIGFqA+qG1qQf7YGAHD3eHYHkXOa3x5Y8s/W4GqDTuJqiLrGwELUB+bpoOOiAxAX6it1OUS9EhfqizGRahiMomU8FpGjYWAh6iVRFPGv9u6gnyWxdYWcm7lb6N9FVySuhKhrDCxEvXS8XIvTVQ3wVMgs+7IQOas7xw6Ch1zAsTItjpdrpC6HqBMGFqJeMreuzEoIh9qLS/GTcwvy8URGgmkPrA++KZW4GqLOGFiIekHfZsTH7X39P+NgW3IR902IAgB8VFyOllauyUKOhYGFqBf2nK5GXZMeoX5KpA8NkbocIpuYMiQEA9UqaK63YudxrslCjoWBhagXctqbzO8aNwgKOX+MyDXIZQJ+lmxqZfngMLuFyLHwNy2Rlcrrr+PL09UAgPvbm9CJXMW9SZEQBOCrc7UorWuWuhwii14FlrVr1yI2NhYqlQpJSUnYt29ft+dWVFTgwQcfxPDhwyGTybB8+fIuz9u6dSsSEhKgVCqRkJCAbdu29aY0Irv74HApjCKQEhuEm7j2CrmYqCBvTI4zdXN+yFYWciBWB5acnBwsX74cq1atQlFREdLT0zF37lyUlJR0eb5Op0NoaChWrVqFMWPGdHlOQUEBMjMzkZWVhSNHjiArKwv33XcfDh48aG15RHZlMIqWGRQPpkRLXA2RfZgH335YeAUGoyhxNUQmgiiKVn03pqSkYPz48Vi3bp3l2IgRIzB//nxkZ2ff8Lk333wzxo4dizVr1nQ4npmZCa1Wix07dliOzZkzB4GBgdi8eXOP6tJqtVCr1dBoNPD39+/5DRFZ4ctT1fjFxm8Q4O2Br1fOhMpDLnVJRDbX0mpAyh8+h+Z6Kzb+YgJuHh4mdUnkwnr6+m1VC4ter0dhYSEyMjI6HM/IyMCBAwd6VylMLSw/vubs2bNveE2dTgetVtvhQWRv7x8ytSTePS6SYYVclspDbln5NodrspCDsCqw1NTUwGAwIDw8vMPx8PBwVFb2fgpcZWWl1dfMzs6GWq22PKKiOPiR7KtK24IvTpkG2z4wkd9v5Nrub/8e33WiClXaFomrIerloFtBEDq8L4pip2P2vubKlSuh0Wgsj9JS/hVA9vXh4VIYjCKSYwIxNNxP6nKI7Co+wh8TBwfBYBSx+VDXYxSJ+pNVgSUkJARyubxTy0d1dXWnFhJrREREWH1NpVIJf3//Dg8iezH90jaF4gcmcrAtuYcFqTEAgM2HStBqMEpcDbk7qwKLp6cnkpKSkJeX1+F4Xl4e0tLSel1Eampqp2vu2rWrT9cksqXPT1ahrP46Arw9cNvoAVKXQ9Qv5oyMQIivJ6q0Ouw+USV1OeTmFNY+YcWKFcjKykJycjJSU1OxYcMGlJSUYMmSJQBMXTVlZWXYtGmT5TnFxcUAgMbGRly9ehXFxcXw9PREQkICAGDZsmWYOnUqXnnlFcybNw/bt2/H7t27sX//fhvcIlHfbSq4DADInBDFwbbkNjwVMtw/IRp/+fIc/v71ZcwdxbBO0rE6sGRmZqK2tharV69GRUUFEhMTkZubi5gYU9NhRUVFpzVZxo0bZ/l3YWEh3n//fcTExODSpUsAgLS0NGzZsgXPPfccnn/+ecTFxSEnJwcpKSl9uDUi2zhX3YD952ogE4CsSTFSl0PUrx5IicbaPedw4HwtzlU3YEgYx2+RNKxeh8VRcR0WspffbD+GTQWXkZEQjg0Lk6Uuh6jfPbrpMPJOVOHhtMF48c6RUpdDLsYu67AQuZuGllZsLbwCAHgobbC0xRBJxNyyuLXwCpp0bRJXQ+6KgYXoBrYWXkGT3oAhYb5IiwuWuhwiSUwZEoLYEB806Nrwr/YAT9TfGFiIumE0ipbBtg+lxvR5rSEiZyWTCXhk8mAAwLtfXeT+QiQJBhaibuSfvYoLNU3wUypw9/hIqcshktQ9SZFQe3ngcm0zPj/JKc7U/xhYiLqxIf8CANPOtT5KqyfUEbkUb0+FZYfyt/dflLgackcMLERdOFamwYHztZDLBDwyJVbqcogcwkOpg6GQCTh0sQ5Hr2ikLofcDAMLURf+us/UunLH6AEYFOAlcTVEjiFCrcLt7Ss9v7P/gsTVkLthYCH6kSvXmvHpdxUAgMXpN0lcDZFjWTTF9DPx6XcVqNRwF2fqPwwsRD/y3leXYDCKmDwkGImD1FKXQ+RQRkWqkRIbhDajiHe/4lgW6j8MLEQ/oLneii2HTFtLPMrWFaIuPT7N9LPxz68vo75ZL3E15C4YWIh+4P2DJWjSGzA83A/ThoVKXQ6RQ5o+PAzxEX5o0hvwtwOXpS6H3AQDC1G763qDZSDhY1Nv4kJxRN0QBAFLpw8BALx34CKX66d+wcBC1O79QyWoadQjKsgLd44dKHU5RA7t1lEDEBvig/rmVrx/sETqcsgNMLAQAWhpNWD93vMAgF/ePAQecv5oEN2IXCbgiWlxAEzLALS0GiSuiFwdfysTAfjgcCmqG3QYqFbhHi7DT9Qj88cNwgC1CtUNOmz9lpsikn0xsJDb07cZ8dYeU+vKEzfHwVPBHwuinvBUyPDYVNOMoXV7zkPfZpS4InJl/M1Mbm/rt1dQrmlBmJ8S9yZHSV0OkVO5f0I0Qv2UuHLtOj4sLJW6HHJhDCzk1vRtRqzdcw4A8Pi0OKg85BJXRORcvDzlWHqzaSzLG5+f41gWshsGFnJrOd+UoLTuOkJ8lXhwYrTU5RA5pQdSojFQrUKltgX/5IwhshMGFnJbzfo2/PlzU+vKsplD4OXJ1hWi3lAq5Hhq5lAAwLo957guC9kFAwu5rfe+uoSaRh2ig7yROYGtK0R98bOkSMQEe6OmUY+/FVySuhxyQQws5Jbqm/V4q33dlRWzhnFmEFEfechlWH6LqZVl/d4L0La0SlwRuRr+lia3tG7veTS0tCE+wg93juGqtkS2cOeYQRgS5gvN9Vas/fK81OWQi2FgIbdTqWnBxq8uAQB+NWc4ZDLuGURkC3KZgGfnxAMA3v3qIkrrmiWuiFwJAwu5nf/beRq6NiOSYwIxfXiY1OUQuZSZI8KQFhcMfZsR/7vztNTlkAthYCG3cqS03rKE+HO3J3BHZiIbEwQBq24bAUEAPjlSjqKSa1KXRC6CgYXchiiKeOmT4wCAu8cPwtioAGkLInJRIweqLXty/e4/JyGKosQVkStgYCG38fGRcnxbUg9vTzmeae9nJyL7+H8Zw+HlIUfh5WvIPVopdTnkAhhYyC0069uQnXsKALB0+hCE+6skrojItUWoVZaNEX//nxNcTI76jIGF3MJbe86jUtuCyEAvLJoSK3U5RG5hybQ4RAZ6oVzTgte/OCt1OeTkGFjI5Z2rbsRbey8AAFbdOoIbHBL1Ey9POV66cyQA4J19F3G6skHiisiZ9SqwrF27FrGxsVCpVEhKSsK+fftueP7evXuRlJQElUqFm266CW+99VaHj2/cuBGCIHR6tLS09KY8IgtRFLFq21HoDUbcPDwUcxIjpC6JyK3MHBGOWQnhaDOKeP6jYxyAS71mdWDJycnB8uXLsWrVKhQVFSE9PR1z585FSUnXO3RevHgRt956K9LT01FUVIRf//rX+K//+i9s3bq1w3n+/v6oqKjo8FCpOM6A+ubDw1dw8GIdvDzk+O28RE5jJpLAC3ckwMtDjkOX6rD12zKpyyEnZXVgee2117Bo0SIsXrwYI0aMwJo1axAVFYV169Z1ef5bb72F6OhorFmzBiNGjMDixYvxyCOP4NVXX+1wniAIiIiI6PAg6ouaRh1+n3sSAPD0rKGICvKWuCIi9xQZ6I3/at/N+Q+5J1HbqJO4InJGVgUWvV6PwsJCZGRkdDiekZGBAwcOdPmcgoKCTufPnj0bhw8fRmvr95tjNTY2IiYmBpGRkbj99ttRVFR0w1p0Oh20Wm2HB9EP/e7TE9Bcb0XCAH88MpkDbYmktGhKLIaH+6GuSY/ffHxc6nLICVkVWGpqamAwGBAeHt7heHh4OCoru55nX1lZ2eX5bW1tqKmpAQDEx8dj48aN+Pjjj7F582aoVCpMnjwZZ892P6o8OzsbarXa8oiKirLmVsjFfX6yCh8Vl0MmANl3j4JCzvHlRFLyVMjw6r1jIJcJ+M93FfjPdxVSl0ROple/xX88DkAUxRuODejq/B8enzRpEhYsWIAxY8YgPT0dH3zwAYYNG4Y33nij22uuXLkSGo3G8igtLe3NrZALqmvS45mtRwGY/qobwxVtiRzCqEg1fnlzHADg+e3HUMOuIbKCVYElJCQEcrm8U2tKdXV1p1YUs4iIiC7PVygUCA4O7roomQwTJky4YQuLUqmEv79/hweRKIp47qOjqGnUYWiYL/47Y7jUJRHRDzw1YyjiI9q7hrYfk7occiJWBRZPT08kJSUhLy+vw/G8vDykpaV1+ZzU1NRO5+/atQvJycnw8PDo8jmiKKK4uBgDBgywpjwifHykHLlHK6GQCXjtvrFcc4XIwZi7hhQyAblHK7G9mLOGqGes7hJasWIF3n77bbz77rs4efIknn76aZSUlGDJkiUATF01CxcutJy/ZMkSXL58GStWrMDJkyfx7rvv4p133sH/+3//z3LOSy+9hJ07d+LChQsoLi7GokWLUFxcbLkmUU+U1jXj+Y9Mf7E9NWMoRkWqJa6IiLqSOEiNJ2cMAQCs2nYMl2qaJK6InIHC2idkZmaitrYWq1evRkVFBRITE5Gbm4uYmBgAQEVFRYc1WWJjY5Gbm4unn34ab775JgYOHIjXX38d99xzj+Wc+vp6PPbYY6isrIRarca4ceOQn5+PiRMn2uAWyR3o24x4anMRtC1tGBsVgF9Oj5O6JCK6gSenD8GBc7U4dKkOT20uwr+eSIVSwRZR6p4gusiyg1qtFmq1GhqNhuNZ3NAfck9iQ/4F+KsU+M9/pXPNFSInUKG5jlv/vA/XmlvxyORY/OaOBKlLIgn09PWbcz3J6X1xqgob8k17Bf3fvWMYVoicxAC1F169dwwA4N2vLmL3iSqJKyJHxsBCTu1STROWbykGADycNhizR3KFZCJnMnNEuGVhxxUfFOMix7NQNxhYyGk16trw6KbD0La0YVx0AFbeGi91SUTUC8/OjUdSTCC0LW1Y/Ldv0NDS+tNPIrfDwEJOyWgUsSKnGGerGxHmp8RbC5I4YI/ISXkqZFi3YDwi/FU4f9XUamowusTwSrIhBhZySmt2n8GuE1XwlMuwPisJ4f7c2ZvImYX5qbBhYRKUChk+P1WNP+46LXVJ5GAYWMjp5HxTgte/OAcA+N1diRgXHShxRURkC6MjA/DKPaMBAGv3nEfONyU/8QxyJwws5FS+PF2NX28zLQ735PQhuC+Zm14SuZL54wZZ9hta+e+jnDlEFgws5DSOlNZj6T+/hcEo4u7xg/DfGcOkLomI7OB/Zg/HvUmRMIrA0ve/ReHlOqlLIgfAwEJO4US5FgvfPYRmvQGThwTj5btH33CHcCJyXoIgIPvuUZgZHwZdmxGPbDyM05UNUpdFEmNgIYd3tqoBWe8chOZ6K8ZFB2B9VjI8FfzWJXJlCrkMf3lwPMZHB0BzvRUP/vVrhhY3x9/65NDOVTfi528fRG2THomD/LHxFxPhq7R6CywickJennK8+/AEJA7yR22THg/+9WucqtRKXRZJhIGFHNbxcg0y1xegukGH4eF++PsjKVB7eUhdFhH1owBvT/xjUQpGDVK3h5aDOFnB0OKOGFjIIRVevob7N3xtaVnZ/NgkBPp4Sl0WEUnAHFpGR6pR16TH/Ru+xjeXOBDX3TCwkMPZdbwSC94+iIaWNiTHBOL9RychiGGFyK2pvT3w90UpljEtP3/7IHYcrZC6LOpHDCzkMERRxF/zL+DxfxTieqsBU4eFYtOiifBXsRuIiAC1lwf+uXgSZiWEQ99mxC/f/xbvfXVR6rKonzCwkENoNRix6qNj+H3uSYgi8POUaLz7UDK8PTnAloi+5+Upx1sLkrBgUjREEXjpkxNY+e+j0LUZpC6N7IyvBiS5Cs11PPl+EQovX4MgAM/dloBHJg/mOitE1CW5TMBv5yUiMtAbr3x2CpsPleBEhRbrfj4eAwO8pC6P7IQtLCSpPaercdvr+1F4+Rr8lAr8NSsZi6bEMqwQ0Q0JgoAl0+Lw3sMToPbywJHSetzxxn7sP1sjdWlkJwwsJAldmwGvfHYKv9j4Deqa9Bg50B+f/tcU3JIQLnVpROREbh4ehk+fmoKEAaa1Wha8cxC//fQEWlrZReRqGFio3313xfSX0Lo95yGKwIJJ0dj6RBpign2kLo2InFBUkDe2PpGGB1OiAQDv7L+IO97Yj2NlGokrI1sSRFEUpS7CFrRaLdRqNTQaDfz9/aUuh7rQ0mrAG1+cxVt7L8BgFBHi64nfzU/EnMQBUpdGRC7ii1NV+NW/jqKmUQeFTMCi9FgsmzmUA/gdWE9fvxlYyO5EUcTO45X47acnUVZ/HQBw++gBWD0vkeurEJHN1Tbq8NxHx7DjWCUAYFCAF164IwEZIyMkroy6wsBCDuFUpRa/+/Qk9p8zDYQboFbhhTsS2KpCRHb3+ckq/Gb7ccsfSlOGhOCZOfEYFamWuDL6IQYWktT5q41Ys/ssPv2uHKIIeCpkeHzqTXji5jg2zRJRv7muN3VFv73vIvQGIwDgjjEDsWLWMMSGcNycI2BgIUmcKNfi7X0X8FFxGYzt31m3jR6AZ2bHIzrYW9riiMhtldY147W8M/iouAyiCMgE4NZRA/DEzXEYOZAtLlJiYKF+YzSK2HvmKt7efwFfnau1HL9lRDhWzBqGhIH8ehCRYzhersGrO0/jy9NXLcemDQvFQ2kxmDYsDHIZ14DqbwwsZHfl9dfx72+v4F+FV3CpthmAaQXKuYkReDT9JoyJCpC2QCKibhwv12DdnvPIPVphaQ0eFOCFByZG4b7kKIT5q6Qt0I0wsJBdaK634vOTVdhWVIb952pg/u7xUyrwQEo0HkobjEFcGpuInMSlmib84+vL+LDwCjTXWwGYuosmDwnBHaMHYvbICKi9uQGrPTGwkM1Ualrw+akqfHasEgXna9Fm/P5bJiU2CPcmR2FuYgR8lBxMS0TOqaXVgNyjFfjnwRIUXr5mOe4hF5A+NBTTh4fi5uFhiAriWDxbY2ChXtO2tOLr87X46lwN9p+rwfmrTR0+PizcF3MSB+Ce8YO4Oi0RuZxLNU34z9EKfHKkHKcqGzp87KZQH9w8LAxpccFIiglEINeS6jMGFuqRVoMRpysbcORKPYpL6nHkSj3OVjfih98VMgEYHRmA2SMjMHtkOG4K9ZWuYCKifnSmqgF5J6qw9/RVFJZcg8HY8SVzSJgvkmMCMT4mEAkD/DE03BdKhVyiap2TXQPL2rVr8X//93+oqKjAyJEjsWbNGqSnp3d7/t69e7FixQocP34cAwcOxK9+9SssWbKkwzlbt27F888/j/PnzyMuLg6///3vcdddd/W4JgaWG2s1GFF27TrOVjfiTFUDzlY14Gx1I85VN0LXZux0/k0hPpg8JASTh4Qg9aZg9uESkdvTXG/FV+dqkH/mKr65VNep9RkAFDIBQ8J8kTDAH/ED/BAb4ovBwd6ICvKGyoNBpis9ff22etBBTk4Oli9fjrVr12Ly5MlYv3495s6dixMnTiA6OrrT+RcvXsStt96KRx99FP/4xz/w1Vdf4Ze//CVCQ0Nxzz33AAAKCgqQmZmJ3/72t7jrrruwbds23Hfffdi/fz9SUlKsLdHtGIwiapt0qGnQo7ZJhyqtDqV1zbhy7TpKrzWj7Np1VGiuw9hNNPVTKTA2KgBjIgMwJioAY6LUCPPjCHkioh9Se3ng1lEDcOso00rddU16FF6+hsOX6vDdFQ1OVGihud6KU5UNpq6kou+fKwjAQLUXYkN8EBnohXB/FSLU7Q9/0yPA2wOCwGnV3bG6hSUlJQXjx4/HunXrLMdGjBiB+fPnIzs7u9P5zzzzDD7++GOcPHnScmzJkiU4cuQICgoKAACZmZnQarXYsWOH5Zw5c+YgMDAQmzdv7lFdztjCIooiWg0idG0GtLQaLW9bWg1oaGlDQ0trh7eNujZo29+/1qxHTYMeNY061DXr0ZOvolIhQ1yoL4aG+2JYuB+GhpneRgd5Q8a1B4iI+kQURVRoWnCiXIsTFVqcqWrApdomXKppRqOu7Sef7yEXEODtiUBvD8vbQG9PBHh7IsDbA75KBXyUcnh7KuDjqYC3Ug5fpQLennL4eCrg5SmHUiFzutBjlxYWvV6PwsJCPPvssx2OZ2Rk4MCBA10+p6CgABkZGR2OzZ49G++88w5aW1vh4eGBgoICPP30053OWbNmjTXl2cU7+y+itK4ZBqOINqMIg9EIgxEwGI3t73//aDOKMIoi2gzm940wiKZzW9s6BxNdm6HbVg9rCQIQ7OOJYB8lwvyViAz0QmSgt+VtVKAXQnyVDCZERHYiCAIGBnhhYIAXbkkItxwXRRG1TXpcqmnCxZomlNe3oFLbgiptCyo1pn/XNenRahBxtUGHqw26PtXhKZfBQy7AUyGzPDzkMnjKZVCa/62QQS4ToJAJkMsEyAQBCrnprVwmQG5+KxMg+8H7i6bESjZTyqrAUlNTA4PBgPDw8A7Hw8PDUVlZ2eVzKisruzy/ra0NNTU1GDBgQLfndHdNANDpdNDpvv+iarVaa26lxz79rhxFJfV2ufaPqTxkUCrkUHnI4KtUwE/lAT+VAv7tb/1UCvgqTf8O9PFAiK/S8gjy8eQKjUREDkgQBMvv6uTBQV2eo2szoLZRj2vNetQ3t6KuSY/6Zj2uNZta1DXNrWjSt6FZb0CTrg1NOkOH9384FlFvMEJvAJr0Bpvfy51jBzpHYDH7cXOTKIo3bILq6vwfH7f2mtnZ2XjppZd6XHNv3TM+EpPjQixJVPaDRPp9OpV1+bEfpleFTAaVhwwqD1OTnfmt0sMUUDzlzteMR0REtqFUyC2tM73RZjCiudUAfZsR+jYjWg2mt7o2I/QGI1rb35o/rjcYv+8ZMIowiKa35p4DoyhaehMMRsAgmnoYIiRcAdiqwBISEgK5XN6p5aO6urpTC4lZREREl+crFAoEBwff8JzurgkAK1euxIoVKyzva7VaREVFWXM7PbJgUozNr0lERGRLCrkM/nKZ1GXYlVV35+npiaSkJOTl5XU4npeXh7S0tC6fk5qa2un8Xbt2ITk5GR4eHjc8p7trAoBSqYS/v3+HBxEREbkmq7uEVqxYgaysLCQnJyM1NRUbNmxASUmJZV2VlStXoqysDJs2bQJgmhH0l7/8BStWrMCjjz6KgoICvPPOOx1m/yxbtgxTp07FK6+8gnnz5mH79u3YvXs39u/fb6PbJCIiImdmdWDJzMxEbW0tVq9ejYqKCiQmJiI3NxcxMaauk4qKCpSUlFjOj42NRW5uLp5++mm8+eabGDhwIF5//XXLGiwAkJaWhi1btuC5557D888/j7i4OOTk5HANFiIiIgLApfmJiIhIQj19/XbtETpERETkEhhYiIiIyOExsBAREZHDY2AhIiIih8fAQkRERA6PgYWIiIgcHgMLEREROTwGFiIiInJ4DCxERETk8Kxemt9RmRfs1Wq1EldCREREPWV+3f6phfddJrA0NDQAAKKioiSuhIiIiKzV0NAAtVrd7cddZi8ho9GI8vJy+Pn5QRAEm11Xq9UiKioKpaWlLrtHkavfo6vfH+D698j7c36ufo+ufn+A/e5RFEU0NDRg4MCBkMm6H6niMi0sMpkMkZGRdru+v7+/y34Tmrn6Pbr6/QGuf4+8P+fn6vfo6vcH2Oceb9SyYsZBt0REROTwGFiIiIjI4TGw/ASlUokXXngBSqVS6lLsxtXv0dXvD3D9e+T9OT9Xv0dXvz9A+nt0mUG3RERE5LrYwkJEREQOj4GFiIiIHB4DCxERETk8BhYiIiJyeAwsvaTT6TB27FgIgoDi4mKpy7GZO++8E9HR0VCpVBgwYACysrJQXl4udVk2cenSJSxatAixsbHw8vJCXFwcXnjhBej1eqlLs6nf//73SEtLg7e3NwICAqQup8/Wrl2L2NhYqFQqJCUlYd++fVKXZFP5+fm44447MHDgQAiCgI8++kjqkmwmOzsbEyZMgJ+fH8LCwjB//nycPn1a6rJsat26dRg9erRlMbXU1FTs2LFD6rLsJjs7G4IgYPny5f3+uRlYeulXv/oVBg4cKHUZNjd9+nR88MEHOH36NLZu3Yrz58/jZz/7mdRl2cSpU6dgNBqxfv16HD9+HH/605/w1ltv4de//rXUpdmUXq/HvffeiyeeeELqUvosJycHy5cvx6pVq1BUVIT09HTMnTsXJSUlUpdmM01NTRgzZgz+8pe/SF2Kze3duxdLly7F119/jby8PLS1tSEjIwNNTU1Sl2YzkZGRePnll3H48GEcPnwYM2bMwLx583D8+HGpS7O5b775Bhs2bMDo0aOlKUAkq+Xm5orx8fHi8ePHRQBiUVGR1CXZzfbt20VBEES9Xi91KXbxv//7v2JsbKzUZdjFe++9J6rVaqnL6JOJEyeKS5Ys6XAsPj5efPbZZyWqyL4AiNu2bZO6DLuprq4WAYh79+6VuhS7CgwMFN9++22py7CphoYGcejQoWJeXp44bdo0cdmyZf1eA1tYrFRVVYVHH30Uf//73+Ht7S11OXZVV1eHf/7zn0hLS4OHh4fU5diFRqNBUFCQ1GVQF/R6PQoLC5GRkdHheEZGBg4cOCBRVdQXGo0GAFz2Z85gMGDLli1oampCamqq1OXY1NKlS3HbbbfhlltukawGBhYriKKIhx9+GEuWLEFycrLU5djNM888Ax8fHwQHB6OkpATbt2+XuiS7OH/+PN544w0sWbJE6lKoCzU1NTAYDAgPD+9wPDw8HJWVlRJVRb0liiJWrFiBKVOmIDExUepybOro0aPw9fWFUqnEkiVLsG3bNiQkJEhdls1s2bIF3377LbKzsyWtg4EFwIsvvghBEG74OHz4MN544w1otVqsXLlS6pKt0tP7M/uf//kfFBUVYdeuXZDL5Vi4cCFEB14Q2dr7A4Dy8nLMmTMH9957LxYvXixR5T3Xm3t0FYIgdHhfFMVOx8jxPfnkk/juu++wefNmqUuxueHDh6O4uBhff/01nnjiCTz00EM4ceKE1GXZRGlpKZYtW4Z//OMfUKlUktbCpflh+kuupqbmhucMHjwY999/Pz755JMOvywNBgPkcjl+/vOf429/+5u9S+2Vnt5fV9+MV65cQVRUFA4cOOCwTZzW3l95eTmmT5+OlJQUbNy4ETKZ4+f23nwNN27ciOXLl6O+vt7O1dmHXq+Ht7c3PvzwQ9x1112W48uWLUNxcTH27t0rYXX2IQgCtm3bhvnz50tdik099dRT+Oijj5Cfn4/Y2Fipy7G7W265BXFxcVi/fr3UpfTZRx99hLvuugtyudxyzGAwQBAEyGQy6HS6Dh+zJ0W/fBYHFxISgpCQkJ887/XXX8fvfvc7y/vl5eWYPXs2cnJykJKSYs8S+6Sn99cVc57V6XS2LMmmrLm/srIyTJ8+HUlJSXjvvfecIqwAffsaOitPT08kJSUhLy+vQ2DJy8vDvHnzJKyMekoURTz11FPYtm0b9uzZ4xZhBTDdtyP/zrTGzJkzcfTo0Q7HfvGLXyA+Ph7PPPNMv4UVgIHFKtHR0R3e9/X1BQDExcUhMjJSipJs6tChQzh06BCmTJmCwMBAXLhwAb/5zW8QFxfnsK0r1igvL8fNN9+M6OhovPrqq7h69arlYxERERJWZlslJSWoq6tDSUkJDAaDZZ2gIUOGWL5nncWKFSuQlZWF5ORkpKamYsOGDSgpKXGpcUeNjY04d+6c5f2LFy+iuLgYQUFBnX7nOJulS5fi/fffx/bt2+Hn52cZe6RWq+Hl5SVxdbbx61//GnPnzkVUVBQaGhqwZcsW7NmzB5999pnUpdmEn59fpzFH5jGO/T4Wqd/nJbmQixcvutS05u+++06cPn26GBQUJCqVSnHw4MHikiVLxCtXrkhdmk289957IoAuH67koYce6vIev/zyS6lL65U333xTjImJET09PcXx48e73JTYL7/8ssuv10MPPSR1aX3W3c/be++9J3VpNvPII49Yvj9DQ0PFmTNnirt27ZK6LLuSalozx7AQERGRw3OODnwiIiJyawwsRERE5PAYWIiIiMjhMbAQERGRw2NgISIiIofHwEJEREQOj4GFiIiIHB4DCxERETk8BhYiIiJyeAwsRERE5PAYWIiIiMjhMbAQERGRw/v/tkzOVTZwT6IAAAAASUVORK5CYII=\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Import\\n\",\n \"import matplotlib as mpl\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Import the stats library\\n\",\n \"from scipy import stats\\n\",\n \"\\n\",\n \"# Set the mean\\n\",\n \"mean = 0\\n\",\n \"\\n\",\n \"#Set the standard deviation\\n\",\n \"std = 1\\n\",\n \"\\n\",\n \"\\n\",\n \"# Create a range\\n\",\n \"X = np.arange(-4,4,0.01)\\n\",\n \"\\n\",\n \"#Create the normal distribution for the range\\n\",\n \"Y = stats.norm.pdf(X,mean,std)\\n\",\n \"\\n\",\n \"#\\n\",\n \"plt.plot(X,Y)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's learn how to use numpy to create the normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [],\n \"source\": [\n \"#Set the mean and the standard deviaiton\\n\",\n \"mu,sigma = 0,0.1\\n\",\n \"\\n\",\n \"# Now grab 1000 random numbers from the normal distribution\\n\",\n \"norm_set = np.random.normal(mu,sigma,1000)\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n },\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"(array([ 1., 1., 0., 0., 0., 1., 1., 2., 4., 4., 7., 6., 7.,\\n\",\n \" 5., 12., 12., 25., 32., 29., 40., 34., 42., 52., 42., 47., 58.,\\n\",\n \" 72., 52., 55., 39., 42., 49., 32., 36., 27., 20., 26., 18., 19.,\\n\",\n \" 13., 15., 6., 5., 2., 3., 1., 1., 1., 0., 2.]),\\n\",\n \" array([-0.356904 , -0.34361366, -0.33032332, -0.31703298, -0.30374264,\\n\",\n \" -0.29045229, -0.27716195, -0.26387161, -0.25058127, -0.23729092,\\n\",\n \" -0.22400058, -0.21071024, -0.1974199 , -0.18412956, -0.17083921,\\n\",\n \" -0.15754887, -0.14425853, -0.13096819, -0.11767784, -0.1043875 ,\\n\",\n \" -0.09109716, -0.07780682, -0.06451648, -0.05122613, -0.03793579,\\n\",\n \" -0.02464545, -0.01135511, 0.00193524, 0.01522558, 0.02851592,\\n\",\n \" 0.04180626, 0.05509661, 0.06838695, 0.08167729, 0.09496763,\\n\",\n \" 0.10825797, 0.12154832, 0.13483866, 0.148129 , 0.16141934,\\n\",\n \" 0.17470969, 0.18800003, 0.20129037, 0.21458071, 0.22787105,\\n\",\n \" 0.2411614 , 0.25445174, 0.26774208, 0.28103242, 0.29432277,\\n\",\n \" 0.30761311]),\\n\",\n \" )\"\n ]\n },\n \"execution_count\": 30,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Now let's plot it using seaborn\\n\",\n \"\\n\",\n \"import seaborn as sns\\n\",\n \"\\n\",\n \"plt.hist(norm_set,bins=50)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"There's a ton on information to go over for the normal distribution, this notebook should just serve as a very mild introduction, for more info check out the following sources:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Normal_distribution\\n\",\n \"\\n\",\n \"2.) http://mathworld.wolfram.com/NormalDistribution.html\\n\",\n \"\\n\",\n \"3.) http://stattrek.com/probability-distributions/normal.aspx\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Thanks!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Poisson Distribution.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about the Poisson Distribution! \\n\",\n \"Note: I suggest you learn about the binomial distribution first.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"A poisson distribution focuses on the number of discrete events or occurrences over a specified interval or continuum (e.g. time,length,distance,etc.). We'll look at the formal definition, get a break down of what that actually means, see an example and then look at the other characteristics such as mean and standard deviation.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Formal Definition: A discrete random variable X has a Poisson distribution with parameter λ if for k=0,1,2.., the probability mass function of X is given by:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"$$Pr(X=k)=\\\\frac{\\\\lambda^ke^{-\\\\lambda}}{k!}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"where e is Euler's number (e=2.718...) and k! is the factorial of k.\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The Poisson Distribution has the following characteristics:\\n\",\n \"\\n\",\n \" 1.) Discrete outcomes (x=0,1,2,3...)\\n\",\n \" 2.) The number of occurrences can range from zero to infinity (theoretically). \\n\",\n \" 3.) It describes the distribution of infrequent (rare) events.\\n\",\n \" 4.) Each event is independent of the other events.\\n\",\n \" 5.) Describes discrete events over an interval such as a time or distance.\\n\",\n \" 6.) The expected number of occurrences E(X) are assumed to be constant throughout the experiment.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So what would an example question look like? \\n\",\n \"\\n\",\n \"Let's say a McDonald's has a lunch rush from 12:30pm to 1:00pm. From looking at customer sales from previous days, we know that on average 10 customers enter during 12:30pm to 1:00pm. What is the probability that *exactly* 7 customers enter during lunch rush? What is the probability that *more than* 10 customers arrive? \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's begin by thinking about how many customers we expect to come into McDonald's during lunch rush. Well we were actually already given that information, it's 10. This means that the mean is 10, then our expected value E(X)=10. In the Poisson distribution this is λ. So the mean = λ for a Poisson Distribution, it is the expected number of occurences over the specfied interval.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So since we now know what λ is, we can plug the information into the probability mass function and get an answer, let's use python and see how this works. Let's start off by answering the first question: \\n\",\n \"\\n\",\n \"What is the probability that exactly 7 customers enter during lunch rush?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 45,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" There is a 9.01 % chance that exactly 7 customers show up at the lunch rush\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Note do not use lambda as an object name in python! It is already used for special lambda functions in Python!!\\n\",\n \"\\n\",\n \"# Set lambda\\n\",\n \"lamb = 10\\n\",\n \"\\n\",\n \"# Set k to the number of occurences\\n\",\n \"k=7\\n\",\n \"\\n\",\n \"#Set up e and factorial math statements\\n\",\n \"from math import exp\\n\",\n \"from math import factorial\\n\",\n \"from __future__ import division\\n\",\n \"\\n\",\n \"# Now put the probability mass function\\n\",\n \"prob = (lamb**k)*exp(-lamb)/factorial(k)\\n\",\n \"\\n\",\n \"# Put into percentage form and print answer\\n\",\n \"print( ' There is a %2.2f %% chance that exactly 7 customers show up at the lunch rush' %(100*prob))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we've seen how to create the PMF manually, let's see how to do it automatically with scipy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"There is a 9.01 % chance that exactly 7 customers show up at the lunch rush\\n\",\n \"The mean is 10.00 \\n\"\n ]\n }\n ],\n \"source\": [\n \"# Import the dsitrubtion from scipy.stats\\n\",\n \"from scipy.stats import poisson\\n\",\n \"\\n\",\n \"# Set our mean = 10 customers for the lunch rush\\n\",\n \"mu = 10\\n\",\n \"\\n\",\n \"# Then we can get the mean and variance\\n\",\n \"mean,var = poisson.stats(mu)\\n\",\n \"\\n\",\n \"# We can also calculate the PMF at specific points, such as the odds of exactly 7 customers\\n\",\n \"odds_seven = poisson.pmf(7,mu)\\n\",\n \"\\n\",\n \"#Print\\n\",\n \"print( 'There is a %2.2f %% chance that exactly 7 customers show up at the lunch rush' %(100*odds_seven))\\n\",\n \"\\n\",\n \"# Print the mean\\n\",\n \"print( 'The mean is %2.2f ' %mean)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Awesome! Our manual results match up with scipy's built in stats distribution generator!\\n\",\n \"\\n\",\n \"Now what if we wanted to see the entire distribution? We'll need this information to answer the second question.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# Now let's get the PMF and plot it\\n\",\n \"\\n\",\n \"# First the PMF\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Let's see the PMF for all the way to 30 customers, remeber theoretically an infinite number of customers could show up.\\n\",\n \"k=np.arange(30)\\n\",\n \"\\n\",\n \"# Average of 10 customers for the time interval\\n\",\n \"lamb = 10\\n\",\n \"\\n\",\n \"#The PMF we'll use to plot\\n\",\n \"pmf_pois = poisson.pmf(k,lamb)\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 24,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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NofXt7uxYsWKDMzEy1tbVpxYoVWr58uXbs2OGrGRwc1Lx589TR0aEXXnhB7733njZt2qRp06aFfmYAAGDcsP0poYqKCi1btky5ubmSpMrKSu3Zs0fV1dUqLy8PqK+pqdH06dNVWVkpSUpJSVFLS4vWrVunxYsXS5I2b96sTz75RE1NTYqMjJQkJSYmhnpOAABgnLG1wjI4OKjW1la53W6/cbfbraampqD7NDc3B9TPnz9fLS0tOnnypCTppZdeUnp6uh588EHFxsYqNTVVjz/+uIaGhs7ay8DAgPr7+/02AAAwPtkKLL29vRoaGlJsbKzfeGxsrLxeb9B9vF5v0PpTp06pt7dXkvThhx/qhRde0NDQkOrr67Vy5Uo99dRTWrNmzVl7KS8vV3R0tG9LSEiwcyoAAGAMCelNt2FhYX6PLcsKGDtf/RfHh4eHddVVV2njxo1yuVy66667VFpaqurq6rMes6SkRMeOHfNtXV1doZwKAAAYA2y9hyUmJkbh4eEBqyk9PT0BqyhnxMXFBa2PiIjQ5MmTJUlTp05VZGSkwsPDfTUpKSnyer0aHBxUVFRUwHEdDoccDoed9gEAwBhla4UlKipKLpdLHo/Hb9zj8SgjIyPoPunp6QH1DQ0NSktL873B9gc/+IH+/e9/a3h42Ffz/vvva+rUqUHDCgAAuLTYviVUVFSkZ599Vps3b9bhw4dVWFiozs5O5eXlSTp9q2bp0qW++ry8PB05ckRFRUU6fPiwNm/erNraWj3yyCO+mgceeEB9fX16+OGH9f7772v37t16/PHH9eCDD16EUwQAAGOd7Y81Z2dnq6+vT6tXr1Z3d7dSU1NVX1/v+xhyd3e333eyJCcnq76+XoWFhdqwYYPi4+O1fv1630eaJSkhIUENDQ0qLCzUDTfcoGnTpunhhx/W7373u4twigAAYKwL6dea8/PzlZ+fH/S5LVu2BIzNmTNHBw4cOOcx09PT9eabb4bSDgAAGOf4LSEAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeBGj3QCAS0tS8W5b9R1rF45QJwDGElZYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYL6TAUlVVpeTkZDmdTrlcLu3fv/+c9Y2NjXK5XHI6nZoxY4ZqamrOWrt9+3aFhYXpzjvvDKU1AAAwDtkOLHV1dSooKFBpaana2tqUmZmprKwsdXZ2Bq1vb2/XggULlJmZqba2Nq1YsULLly/Xjh07AmqPHDmiRx55RJmZmfbPBAAAjFu2A0tFRYWWLVum3NxcpaSkqLKyUgkJCaqurg5aX1NTo+nTp6uyslIpKSnKzc3Vfffdp3Xr1vnVDQ0N6Re/+IUee+wxzZgxI7SzAQAA45KtwDI4OKjW1la53W6/cbfbraampqD7NDc3B9TPnz9fLS0tOnnypG9s9erVmjJlipYtW3ZBvQwMDKi/v99vAwAA45OtwNLb26uhoSHFxsb6jcfGxsrr9Qbdx+v1Bq0/deqUent7JUlvvPGGamtrtWnTpgvupby8XNHR0b4tISHBzqkAAIAxJKQ33YaFhfk9tiwrYOx89WfGjx8/rl/+8pfatGmTYmJiLriHkpISHTt2zLd1dXXZOAMAADCWRNgpjomJUXh4eMBqSk9PT8AqyhlxcXFB6yMiIjR58mS9++676ujo0O233+57fnh4+HRzERF67733dM011wQc1+FwyOFw2GkfAACMUbZWWKKiouRyueTxePzGPR6PMjIygu6Tnp4eUN/Q0KC0tDRFRkZq5syZOnTokA4ePOjb7rjjDv3oRz/SwYMHudUDAADsrbBIUlFRkXJycpSWlqb09HRt3LhRnZ2dysvLk3T6Vs3Ro0e1detWSVJeXp6eeeYZFRUV6f7771dzc7Nqa2v1/PPPS5KcTqdSU1P9XuPrX/+6JAWMAwCAS5PtwJKdna2+vj6tXr1a3d3dSk1NVX19vRITEyVJ3d3dft/JkpycrPr6ehUWFmrDhg2Kj4/X+vXrtXjx4ot3FgAAYFyzHVgkKT8/X/n5+UGf27JlS8DYnDlzdODAgQs+frBjYOxIKt5tq75j7cIR6gQAMF7wW0IAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPFC+uI4ABgNfCkhcOlihQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxosY7QYA4H8hqXi3rfqOtQtHqBMAoQhphaWqqkrJyclyOp1yuVzav3//OesbGxvlcrnkdDo1Y8YM1dTU+D2/adMmZWZmatKkSZo0aZLmzp2rt99+O5TWAADAOGQ7sNTV1amgoEClpaVqa2tTZmamsrKy1NnZGbS+vb1dCxYsUGZmptra2rRixQotX75cO3bs8NXs27dPd999t/bu3avm5mZNnz5dbrdbR48eDf3MAADAuGE7sFRUVGjZsmXKzc1VSkqKKisrlZCQoOrq6qD1NTU1mj59uiorK5WSkqLc3Fzdd999Wrduna9m27Ztys/P14033qiZM2dq06ZNGh4e1iuvvBL6mQEAgHHDVmAZHBxUa2ur3G6337jb7VZTU1PQfZqbmwPq58+fr5aWFp08eTLoPidOnNDJkyd15ZVXnrWXgYEB9ff3+20AAGB8shVYent7NTQ0pNjYWL/x2NhYeb3eoPt4vd6g9adOnVJvb2/QfYqLizVt2jTNnTv3rL2Ul5crOjratyUkJNg5FQAAMIaE9KbbsLAwv8eWZQWMna8+2LgkPfHEE3r++ee1c+dOOZ3Osx6zpKREx44d821dXV12TgEAAIwhtj7WHBMTo/Dw8IDVlJ6enoBVlDPi4uKC1kdERGjy5Ml+4+vWrdPjjz+ul19+WTfccMM5e3E4HHI4HHbaBwAAY5StwBIVFSWXyyWPx6Of/vSnvnGPx6NFixYF3Sc9PV1/+ctf/MYaGhqUlpamyMhI39iTTz6p//u//9OePXuUlpZmpy2MAL6zAgBgEtu3hIqKivTss89q8+bNOnz4sAoLC9XZ2am8vDxJp2/VLF261Fefl5enI0eOqKioSIcPH9bmzZtVW1urRx55xFfzxBNPaOXKldq8ebOSkpLk9Xrl9Xr16aefXoRTBAAAY53tb7rNzs5WX1+fVq9ere7ubqWmpqq+vl6JiYmSpO7ubr/vZElOTlZ9fb0KCwu1YcMGxcfHa/369Vq8eLGvpqqqSoODg1qyZInfa5WVlenRRx8N8dQAAMB4EdJX8+fn5ys/Pz/oc1u2bAkYmzNnjg4cOHDW43V0dITSBgAAuETw44cAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjBfSrzUDwKUkqXi37X061i4cgU6ASxcrLAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGixjtBjBykop326rvWLtwhDoBAOCrIbAAwAjjfx6Ar45bQgAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeHzTLQAYjG/JBU5jhQUAABiPwAIAAIxHYAEAAMbjPSyG4/41AAAEFgAYt/gfHownId0SqqqqUnJyspxOp1wul/bv33/O+sbGRrlcLjmdTs2YMUM1NTUBNTt27NCsWbPkcDg0a9Ys7dq1K5TWAADAOGQ7sNTV1amgoEClpaVqa2tTZmamsrKy1NnZGbS+vb1dCxYsUGZmptra2rRixQotX75cO3bs8NU0NzcrOztbOTk5euedd5STk6Of//zneuutt0I/MwAAMG7YviVUUVGhZcuWKTc3V5JUWVmpPXv2qLq6WuXl5QH1NTU1mj59uiorKyVJKSkpamlp0bp167R48WLfMebNm6eSkhJJUklJiRobG1VZWannn38+1HMDAISI20kwja3AMjg4qNbWVhUXF/uNu91uNTU1Bd2nublZbrfbb2z+/Pmqra3VyZMnFRkZqebmZhUWFgbUnAk5wQwMDGhgYMD3+NixY5Kk/v5+O6c04lLL9tje5/89Nt/35+GBE7b2/eL5s6+Z+47ma7Pv/2bf0XxtE/a1+/feF//Ow6XnzNyxLOvchZYNR48etSRZb7zxht/4mjVrrGuvvTboPt/85jetNWvW+I298cYbliTro48+sizLsiIjI61t27b51Wzbts2Kioo6ay9lZWWWJDY2NjY2NrZxsHV1dZ0zg4T0KaGwsDC/x5ZlBYydr/7L43aPWVJSoqKiIt/j4eFhffLJJ5o8efI597tY+vv7lZCQoK6uLk2cOHHEX2+s43rZw/W6cFwre7he9nC9Llyo18qyLB0/flzx8fHnrLMVWGJiYhQeHi6v1+s33tPTo9jY2KD7xMXFBa2PiIjQ5MmTz1lztmNKksPhkMPh8Bv7+te/fqGnctFMnDiRSWwD18serteF41rZw/Wyh+t14UK5VtHR0eetsfUpoaioKLlcLnk8Hr9xj8ejjIyMoPukp6cH1Dc0NCgtLU2RkZHnrDnbMQEAwKXF9i2hoqIi5eTkKC0tTenp6dq4caM6OzuVl5cn6fStmqNHj2rr1q2SpLy8PD3zzDMqKirS/fffr+bmZtXW1vp9+ufhhx/WLbfcoj/84Q9atGiRXnzxRb388st6/fXXL9JpAgCAscx2YMnOzlZfX59Wr16t7u5upaamqr6+XomJiZKk7u5uv+9kSU5OVn19vQoLC7VhwwbFx8dr/fr1vo80S1JGRoa2b9+ulStXatWqVbrmmmtUV1enm2666SKc4shwOBwqKysLuC2F4Lhe9nC9LhzXyh6ulz1crws30tcqzLLO9zkiAACA0cWvNQMAAOMRWAAAgPEILAAAwHgEFgAAYDwCS4iqqqqUnJwsp9Mpl8ul/fv3j3ZLRnr00UcVFhbmt8XFxY12W0Z47bXXdPvttys+Pl5hYWH685//7Pe8ZVl69NFHFR8fr8suu0w//OEP9e67745OswY43/X61a9+FTDXvv/9749Os6OsvLxc3/3ud3XFFVfoqquu0p133qn33nvPr4b59bkLuV7Mr9Oqq6t1ww03+L4cLj09XX/72998z4/kvCKwhKCurk4FBQUqLS1VW1ubMjMzlZWV5fdxbnzuW9/6lrq7u33boUOHRrslI3z22WeaPXu2nnnmmaDPP/HEE6qoqNAzzzyjf/zjH4qLi9O8efN0/Pjx/3GnZjjf9ZKkH//4x35zrb6+/n/YoTkaGxv14IMP6s0335TH49GpU6fkdrv12Wef+WqYX5+7kOslMb8k6eqrr9batWvV0tKilpYW3XrrrVq0aJEvlIzovDrnLw0hqO9973tWXl6e39jMmTOt4uLiUerIXGVlZdbs2bNHuw3jSbJ27drlezw8PGzFxcVZa9eu9Y3997//taKjo62amppR6NAsX75elmVZ9957r7Vo0aJR6cd0PT09liSrsbHRsizm1/l8+XpZFvPrXCZNmmQ9++yzIz6vWGGxaXBwUK2trXK73X7jbrdbTU1No9SV2T744APFx8crOTlZd911lz788MPRbsl47e3t8nq9fvPM4XBozpw5zLNz2Ldvn6666ipde+21uv/++9XT0zPaLRnh2LFjkqQrr7xSEvPrfL58vc5gfvkbGhrS9u3b9dlnnyk9PX3E5xWBxabe3l4NDQ0F/DBjbGxswA84Qrrpppu0detW7dmzR5s2bZLX61VGRob6+vpGuzWjnZlLzLMLl5WVpW3btunVV1/VU089pX/84x+69dZbNTAwMNqtjSrLslRUVKSbb75Zqampkphf5xLseknMry86dOiQLr/8cjkcDuXl5WnXrl2aNWvWiM8r21/Nj9PCwsL8HluWFTCG0/+Rn3H99dcrPT1d11xzjf70pz+pqKhoFDsbG5hnFy47O9v359TUVKWlpSkxMVG7d+/Wz372s1HsbHQ99NBD+uc//xn0t9mYX4HOdr2YX5+77rrrdPDgQf3nP//Rjh07dO+996qxsdH3/EjNK1ZYbIqJiVF4eHhAWuzp6QlIlQj0ta99Tddff70++OCD0W7FaGc+ScU8C93UqVOVmJh4Sc+13/zmN3rppZe0d+9eXX311b5x5ldwZ7tewVzK8ysqKkrf+MY3lJaWpvLycs2ePVtPP/30iM8rAotNUVFRcrlc8ng8fuMej0cZGRmj1NXYMTAwoMOHD2vq1Kmj3YrRkpOTFRcX5zfPBgcH1djYyDy7QH19ferq6rok55plWXrooYe0c+dOvfrqq0pOTvZ7nvnl73zXK5hLeX59mWVZGhgYGPl59ZXftnsJ2r59uxUZGWnV1tZa//rXv6yCggLra1/7mtXR0THarRnnt7/9rbVv3z7rww8/tN58803rJz/5iXXFFVdwrSzLOn78uNXW1ma1tbVZkqyKigqrra3NOnLkiGVZlrV27VorOjra2rlzp3Xo0CHr7rvvtqZOnWr19/ePcuej41zX6/jx49Zvf/tbq6mpyWpvb7f27t1rpaenW9OmTbskr9cDDzxgRUdHW/v27bO6u7t924kTJ3w1zK/Pne96Mb8+V1JSYr322mtWe3u79c9//tNasWKFNWHCBKuhocGyrJGdVwSWEG3YsMFKTEy0oqKirO985zt+H3/D57Kzs62pU6dakZGRVnx8vPWzn/3Mevfdd0e7LSPs3bvXkhSw3XvvvZZlnf7oaVlZmRUXF2c5HA7rlltusQ4dOjS6TY+ic12vEydOWG6325oyZYoVGRlpTZ8+3br33nutzs7O0W57VAS7TpKsP/7xj74a5tfnzne9mF+fu++++3z/9k2ZMsW67bbbfGHFskZ2XoVZlmV99XUaAACAkcN7WAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAw3v8Hm6nnv7pBWZ8AAAAASUVORK5CYII=\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# We can now plot it simply by\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Simply call a barplot\\n\",\n \"plt.bar(k,pmf_pois)\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the question: What is the probability that more than 10 customers arrive? We need to sum up the value of every bar past 10 the 10 customers bar.\\n\",\n \"\\n\",\n \"We can do this by using a Cumulative Distribution Function (CDF). This describes the probability that a random variable X with a given probability distribution (such as the Poisson in this current case) will be found to have a value less than or equal to X.\\n\",\n \"\\n\",\n \"What this means is if we use the CDF to calcualte the probability of 10 or less customers showing up we can take that probability and subtract it from the total probability space, which is just 1 (the sum of all the probabilities for every number of customers).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability that 10 or less customers show up is 58.3 %.\\n\"\n ]\n }\n ],\n \"source\": [\n \"# scipy has a built in cdf we can use\\n\",\n \"\\n\",\n \"# Set out k = 10 for ten customers, set mean = 10 for the average of ten customers during lunch rush.\\n\",\n \"k,mu = 10,10\\n\",\n \"\\n\",\n \"# The probability that 10 or less customers show up is:\\n\",\n \"prob_up_to_ten = poisson.cdf(k,mu)\\n\",\n \"\\n\",\n \"#print\\n\",\n \"print( 'The probability that 10 or less customers show up is %2.1f %%.' %(100*prob_up_to_ten))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can answer the question for *more than* 10 customers. It will be the remaining probability space\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The probability that more than ten customers show up during lunch rush is 41.7 %.\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Sorry for the long object names, but hopefully this makes the thought process very clear\\n\",\n \"prob_more_than_ten = 1 - prob_up_to_ten\\n\",\n \"\\n\",\n \"print( 'The probability that more than ten customers show up during lunch rush is %2.1f %%.' %(100*prob_more_than_ten))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"-----\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"That's it for the basics of the poisson distribution! More free info can be found at these sources:\\n\",\n \"\\n\",\n \"1.)http://en.wikipedia.org/wiki/Poisson_distribution#Definition\\n\",\n \"\\n\",\n \"2.)http://stattrek.com/probability-distributions/poisson.aspx\\n\",\n \"\\n\",\n \"3.)http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Sampling Techniques.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn about sampling theory!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Sampling Theory is a study of relationships exisiting between a population and the samples drawn from the population. For instance, the population may be the entire population of the United States, while the sample may be 1000 people you polled for a survey.\\n\",\n \"\\n\",\n \"There are a ton of important questions we want to ask pertaining to sampling theory, such as whether the observed difference between two samples are due to chance variation or if they are statistically significant. These are sometimes known as *tests of significance*. We'll talk about them later in another iPython notebook.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Random Samples and Numbers\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Samples must be chosen so that they are representative of a population. One method of doing this is by selecting using *random sampling*. This methods means that every member of the population has an euqal chance of being selected. There's lots of ways to create a \\\"random\\\" sampling method, it can be as simple as picking names from a hat, or using pseudorandom number generators such as a Mersenne Twister (the default PRNG for python).\\n\",\n \"\\n\",\n \"Learn more about it at (python 2): https://docs.python.org/2/library/random.html\\n\",\n \"\\n\",\n \"Learn more about it at (python 3): https://docs.python.org/3/library/random.html\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling with and without Replacement\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Drawing samples without replacement from a finite source of samples is considered a finite sampling. Drawing samples from a finite source with replacement can be considered infinite. Such as tossing a coin N number of times, while there are only two possibile outcomes, there is an infinite possibility of any series of heads or tails as N goes to infinity.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Means\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you draw N samples from a finite population of Np samples where Np>N then the mean and the std are denoted as the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean: $$\\\\mu_x=\\\\mu$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation: $$\\\\sigma_x= \\\\frac{\\\\sigma}{\\\\sqrt{N}}\\\\sqrt{ \\\\frac{N_p-N}{N_p-N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This means that we can relate our mean and std from out sample to the total sample population.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Proportions\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If the population is infinite and the probability of succes is denoted as p and probability of failure is q=1-p (just like in a binomial distirbution, like a coin flip). The sampling distribution of proportions then has a mean and standard deviation notes as the following:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean: $$\\\\mu_p=p$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation: $$\\\\sigma_p=\\\\sqrt{\\\\frac{pq}{N}}=\\\\sqrt{\\\\frac{p(1-p)}{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling Distribution of Differences and Sums\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you are given two sample populations N1 and N2 both of which are normally distributed, we can obtain the mean and standard deviation of the sampling distribution of diffrences or sums of the statistics. If S1 is a statistics of N1 and S2 a statistic of N2 we can obtain the mean and standard deviation as follows:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the *differences of the statistics* :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is: $$\\\\mu_{S1-S2}=\\\\mu_{S1}-\\\\mu_{S2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation is: $$ \\\\sigma_{S1-S2}=\\\\sqrt{{\\\\sigma^2}_{S1}+{\\\\sigma^2}_{S2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the *sum of the statistics* :\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The mean is: $$\\\\mu_{S1-S2}=\\\\mu_{S1}+\\\\mu_{S2}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The standard deviation is: $$ \\\\sigma_{S1-S2}=\\\\sqrt{{\\\\sigma^2}_{S1}+{\\\\sigma^2}_{S2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Notice that the standard deviations are summed for both cases, but the means are not!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This is just a quick intro to the topic of sampling theory, check out more here:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Sampling_distribution\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "Statistical Estimation Theory.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "Statistics Overview.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#APPENDIX B- STATISTICS OVERVIEW\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Overview of main topic\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##Example problem or manual creation of distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Use scipy to create or analyze the statistics\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"##Additional resources for learning more about the topic\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The online notebooks can be viewed here:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"http://nbviewer.ipython.org/github/jmportilla/Statistics-Notes/tree/master/\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.7\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "T Distribution (Small Sampling Theory).ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Let's learn the T-distribution! Note: Learn about the normal distribution first!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For previous distributions the sample size was assumed large (N>30). For sample sizes that are less than 30, otherwise (N<30). Note: Sometimes the t-distribution is known as the student distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The t-distribution allows for use of small samples, but does so by sacrificing certainty with a margin-of-error trade-off. The t-distribution takes into account the sample size using n-1 degrees of freedom, which means there is a different t-distribution for every different sample size. If we see the t-distribution against a normal distribution, you'll notice the tail ends increase as the peak get 'squished' down. \\n\",\n \"\\n\",\n \"It's important to note, that as n gets larger, the t-distribution converges into a normal distribution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To further explain degrees of freedom and how it relates tothe t-distribution, you can think of degrees of freedom as an adjustment to the sample size, such as (n-1). This is connected to the idea that we are estimating something of a larger population, in practice it gives a slightly larger margin of error in the estimate.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's define a new variable called t, where\\n\",\n \":\\n\",\n \"$$t=\\\\frac{\\\\overline{X}-\\\\mu}{s}\\\\sqrt{N-1}=\\\\frac{\\\\overline{X}-\\\\mu}{s/\\\\sqrt{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"which is analogous to the z statistic given by $$z=\\\\frac{\\\\overline{X}-\\\\mu}{\\\\sigma/\\\\sqrt{N}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The sampling distribution for t can be obtained:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"source\": [\n \"## $$ f(t) = \\\\frac {\\\\varGamma(\\\\frac{v+1}{2})}{\\\\sqrt{v\\\\pi}\\\\varGamma(\\\\frac{v}{2})} (1+\\\\frac{t^2}{v})^{-\\\\frac{v+1}{2}}$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Where the gamma function is: $$\\\\varGamma(n)=(n-1)!$$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And v is the number of degrees of freedom, typically equal to N-1. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Similar to a z-score table used with a normal distribution, a t-distribution uses a t-table. Knowing the degrees of freedom and the desired cumulative probability (e.g. P(T >= t) ) we can find the value of t. Here is an example of a lookup table for a t-distribution: \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's see how to get the t-distribution in Python using scipy!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"collapsed\": false,\n \"jupyter\": {\n \"outputs_hidden\": false\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 15,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Import for plots\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"%matplotlib inline\\n\",\n \"\\n\",\n \"#Import the stats library\\n\",\n \"from scipy.stats import t\\n\",\n \"\\n\",\n \"#import numpy\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"# Create x range\\n\",\n \"x = np.linspace(-5,5,100)\\n\",\n \"\\n\",\n \"# Create the t distribution with scipy\\n\",\n \"rv = t(3)\\n\",\n \"\\n\",\n \"# Plot the PDF versus the x range\\n\",\n \"plt.plot(x, rv.pdf(x))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Additional resources can be found here:\\n\",\n \"\\n\",\n \"1.) http://en.wikipedia.org/wiki/Student%27s_t-distribution\\n\",\n \"\\n\",\n \"2.) http://mathworld.wolfram.com/Studentst-Distribution.html\\n\",\n \"\\n\",\n \"3.) http://stattrek.com/probability-distributions/t-distribution.aspx\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true,\n \"jupyter\": {\n \"outputs_hidden\": true\n }\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" } ]