# Course: 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

- Basic concepts
- Operations on events
- The law of total probability
- Baye’s theorem
- Repetitive experiments
- Random variable, distribution of the discrete random variable
- Distribution function
- Probability density function
- Expected value, mode, median
- Moments, variance, standard deviation
- Geometric distribution
- Binomial distribution
- Poisson distribution
- Exponential distribution
- Uniform distribution
- Normal distribution
- Chi-Squared distribution
- Multivariate random variable, the distribution function
- Multivariate random variable, probability density
- Multivariate random variable, dependent and independent systems of random variables
- Multivariate random variable, numerical characteristics

# Statistics

- Law of large numbers and Chebyshev’s inequality
- Central limit theorem
- Empirical distribution function
- Histogram
- Numerical characteristics for statistical distribution
- Inferential statistics, point estimation
- Method of moments
- Maximum likelihood estimation
- Hypothesis testing basics
- Hypothesis testing, power of the test
- Pearson’s chi-squared test
- Kolmogorov-Smirnov test
- Confidence interval for the mean(sigma known)
- Confidence interval for the mean(sigma not known)

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