Probability Theory and Statistics with Python


At the moment of writing, I am 20 years old software engineer and computer science student. In the last two years, I learned more than during all my conscious living before that. One of the most important things that I realized being a student and software engineer was the importance of a deep understanding of the basic concepts of complex subjects. Especially in those, you spend life doing. Once in university was a course about probability theory. In the process of learning, I left notes and visualizations in the Jupiter notebook. The goal was to build a good understanding of basics while making real word applications modeling. After some time, I realize that my drafts may be better than traditional formal representation, which we usually see in a university. Therefore I moved my notes to the blog.

Table of Content

1. Basic Concepts

2. Operations on Events

3. The Law Of Total Probability

4. Bayes’ Theorem

5. Repetitive experiments

6. Random Variable, Distribution of the Discrete Random Variable

7. Distribution Function

8. Probability Density Function

9. Expected Value, Mode, Median

10. Moments, Variance, Standard Deviation

11. Geometric Distribution

12. Binomial Distribution

13. Poisson Distribution

14. Exponential Distribution

15. Uniform Distribution

16. Normal Distribution

17. Chi-Squared Distribution

18. Multivariate Random Variable - the Distribution Function

19. Multivariate Random Variable - Probability Density

20. Multivariate Random Variable - Systems of Random Variables

21. Multivariate Random Variable - Numerical Characteristics

22. Law of Large Numbers and Chebyshev’s Inequality

23. Central Limit Theorem

24. Empirical Distribution Function

25. Histogram

26. Numerical Characteristics for Statistical Distribution

27. Inferential Statistics and Point Estimation

28. Method of Moments

29. Maximum Likelihood Estimation

30. Hypothesis Testing Basics

31. Hypothesis Testing and Power of the Test

32. Pearson’s Chi-Squared Test

33. Kolmogorov–Smirnov Test

34. Confidence Interval for the Mean(Sigma Known)

35. Confidence Interval for the Mean(Sigma Not Known)