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 # Statistics and Probability in Python 📊 📈 ![license](https://img.shields.io/github/license/Pegah-Ardehkhani/Statistics-and-Probability-in-Python.svg) ![releases](https://img.shields.io/github/release/Pegah-Ardehkhani/Statistics-and-Probability-in-Python.svg)
 > **`Note`**: This repository is still developing.
 <p align="center">
   <img width="500" height="350" src="https://cdn.dribbble.com/users/962944/screenshots/14138307/media/ca3377660c3d2053c9d91ac175871429.gif">
 </p>
 ## Table of content ✍️
 **Chapter 1: Special Continuous Random Variables** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb)
 - 1.1. Normal (Gaussian) Distribution
 - 1.2. Chi-square Distribution
 - 1.3. T-student Distribution
 - 1.4. Fisher Distribution
 - 1.5. Continuous Uniform Distribution
 - 1.6. Exponential Distribution
 - 1.7. Gamma Distribution
 - 1.8. Beta Distribution
 - 1.9. Weibull Distribution
 - 1.10. Cauchy Distribution
 - 1.11. Laplace Distribution
 **Chapter 2: Special Discrete Random Variables** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb)
 - 2.1. Bernoulli Distribution
 - 2.2. Binomial Distribution
 - 2.3. Negative Binomial (Pascal) Distribution
 - 2.4. Geometric Distribution
 - 2.5. Poisson Distribution
 - 2.6. Discrete Uniform Distribution
 - 2.7. Hypergeometric Distribution
 **Chapter 3: Confidence Intervals** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb)
 - 3.1. Confidence Interval for the Mean of a Normal Population
   - 3.1.1. Known Standard Deviation
   - 3.1.2. Unknown Standard Deviation
 - 3.2. Confidence Interval for the Variance of a Normal Population
   - 3.2.1. Unknown Mean of the Population
   - 3.2.2. Known Mean of the Population
 - 3.3. Confidence Interval for the Difference in Means of Two Normal Population
   - 3.3.1. Known Variances
   - 3.3.2. Unknown but Equal Variances
 - 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
 - 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable
 **Chapter 4: Parametric Hypothesis Testing** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb)
 - 4.1. Introduction
 - 4.2. Test Concerning the Mean of a Normal Population
   - 4.2.1. Known Standard Deviation
   - 4.2.2. Unknown Standard Deviation
 - 4.3. Test Concerning the Equality of Means of Two Normal Populations
   - 4.3.1. Known Variances
   - 4.3.2. Unknown but Equal Variances
 - 4.4. Paired t-test
 - 4.5. Test Concerning the Variance of a Normal Population
 - 4.6. Test Concerning the Equality of Variances of Two Normal Populations
 - 4.7. Test Concerning P in Bernoulli Populations
 - 4.8. Test Concerning the Equality of P in Two Bernoulli Populations
 **Chapter 5: Statistical Hypothesis Testing** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb)
 - 5.1. Normality Tests
   - 5.1.1. Shapiro-Wilk Test
   - 5.1.2. D’Agostino’s  Test
   - 5.1.3. Anderson-Darling Test
 - 5.2. Correlation Tests
   - 5.2.1. Pearson’s Correlation Coefficient
   - 5.2.2. Spearman’s Rank Correlation
   - 5.2.3. Kendall’s Rank Correlation
   - 5.2.4. Chi-Squared Test
 - 5.3. Stationary Tests
   - 5.3.1. Augmented Dickey-Fuller Unit Root Test
   - 5.3.2. Kwiatkowski-Phillips-Schmidt-Shin Test
 - 5.4. Other Tests
   - 5.4.1. Mann-Whitney U-Test
   - 5.4.2. Wilcoxon Signed-Rank Test
   - 5.4.3. Kruskal-Wallis H Test
   - 5.4.4. Friedman Test
 **Chapter 6: Regression** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb)
 - 6.1. Introduction
 - 6.2. Least Squares Estimators of the Regression Parameters
 - 6.3. Statistical Inferences about the Regression Parameters
   - 6.3.1. Inferences Concerning  B
     - 6.3.1.1. Known Variance
     - 6.3.1.2. Unknown Variance
   - 6.3.2. Inferences Concerning  A
     - 6.3.2.1. Unknown Variance
   - 6.3.3. T-tests for Regression Parameters with statsmodels
   - 6.3.4. F-statistic for Overall Significance in Regression
 - 6.4. Confidence Intervals Concerning Regression Models
   - 6.4.1. Confidence Interval for  B
     - 6.4.1.1. Known Variance
     - 6.4.1.2. Unknown Variance
   - 6.4.2. Confidence Interval for  A
     - 6.4.2.1. Unknown Variance
   - 6.4.3. Confidence Interval for  A+Bx
     - 6.4.3.1. Unknown Variance
   - 6.4.4. Prediction Interval of a Future Response
 - 6.5. Residuals
   - 6.5.1. Regression Diagnostic
   - 6.5.2. Multicolinearity
 **Chapter 7: Analysis of Variance (ANOVA)** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20(Anova).ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [![nbviewer](https://img.shields.io/badge/render-nbviewer-orange.svg)](http://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20%28Anova%29.ipynb)
 - 7.1. One-Way Analysis of Variance
   - 7.1.1. Equal Sample Sizes
   - 7.1.2. Unequal Sample Sizes
 - 7.2. Two-Way Analysis of Variance