Course of probability theory and mathematical statistics

The book is based on a year-long course of lectures given by the author over several years at the Department of Mathematics of the Mechanics and Mathematics Faculty of Moscow State University. The basic concepts and facts of probability theory are initially introduced for a finite scheme. The mathematical expectation is defined in general as the Lebesgue integral, however, the reader is not assumed to have any prior knowledge of Lebesgue integration. The book includes the following sections: independent trials and Markov chains, limit theorems of Moivre-Laplace and Poisson, random variables, characteristic and generating functions, law of large numbers, central limit theorem, basic concepts of mathematical statistics, hypothesis testing, statistical estimates, confidence intervals. For junior students at universities and technical schools studying probability theory.