The definitions of the probability of random events and the main relationships associated with conditional probabilities and the Bernoulli scheme are given. Various types of random variables, their numerical and functional characteristics, as well as issues related to the convergence of random sequences - the law of large numbers and the central limit theorem are considered.Information is given on Markov random processes and Markov chains with discrete and continuous time, processes with second-order finite moments, processes with independent increments, stationary and ergodic random processes, stochastic integrals and stochastic differential equations. The issues of application of random processes in the analysis of mathematical models of various real objects are considered.The main distributions used in statistics, methods for finding estimates of unknown parameters and properties of estimates, testing of simple and complex hypotheses, sequential and variance analysis, linear regression models.Solutions to more than 130 different typical examples and more than 1100 tasks for independent solution of varying degrees of difficulty are given.For students of higher education institutions. It will be useful for undergraduates and graduate students, teachers, as well as scientific and practical workers.