Probability theory
(HSE, 2019)
The course is taught to 2nd year Bachelor students of Department of Physics of Higher School of Economics, Russia. The aim of the course is to develop skills in working with random variables and processes. The presentation of the formal apparatus is accompanied by an intuitive analysis of the structures and results. At the same time, to determine the objects themselves - a random variable, probability, probability density (probability distribution function) - intuitive ideas are sufficient without any use of measure theory. A special feature of the course is the large number of specific examples of probability distributions, which illustrate general principals. I was a teaching assistant for practical classes in 2019.
| Topic of the seminar | Materials |
|---|---|
| Seminar 1: Mathematical expectation, variance, Bernoulli trial, Binomial distribution, Poisson distribution, Geometric distribution, Negative binomial distribution | notes |
| Seminar 2: Bayes’ theorem, Monty Hall problem, CDF, PDF, Inverse transform sampling, Sum of a random number of random variables | notes |
| Seminar 3: Examples of inverse tranform sampling, Connection between Binomial and Poisson distributions, Connection between Exponential and Poisson distributions, Simularity between Exponential and Geometric distributions, Characteristic function | notes |
| Seminar 4: Rényi thinning, Probability distribution of minimum/maximum | notes |
| Seminar 5: Cauchy distribution, Normal distribution, Beta-function, Gamma-function, Chi-squared distribution | notes |
| Seminar 6: Gaussian distribution, Sample mean, Sample variance | notes |
| Seminar 7: Markov chains, Stationary distribution, Airplane Probability Problem | notes |