Course: Probability Theory and Statistics for Programmers

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Probability Theory and Statistics for Programmers

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 thing that I realized being a student and software engineer was the importance of the deep understanding of 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 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 on Medium. Amount of material will grow with time. If you have ideas about how this can be improved let me know by leaving a comment.🙂

Probability theory

  1. Basic concepts
  2. Operations on events
  3. The law of total probability
  4. Baye’s 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, dependent and independent systems of random variables
  21. Multivariate random variable, numerical characteristics


  1. Law of large numbers and Chebyshev’s inequality
  2. Central limit theorem
  3. Empirical distribution function
  4. Histogram
  5. Numerical characteristics for statistical distribution
  6. Inferential statistics, point estimation
  7. Method of moments
  8. Maximum likelihood estimation
  9. Hypothesis testing basics
  10. Hypothesis testing, power of the test
  11. Pearson’s chi-squared test
  12. Kolmogorov-Smirnov test
  13. Confidence interval for the mean(sigma known)
  14. Confidence interval for the mean(sigma not known)

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