1. 
Title of the discipline (basic disciplines)

BASES OF THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS

2. 
Course of Study

Course 1, specialty Mathematics (research and development activities)

3. 
Semester of training

2 
4. 
Amount of credits

2 
5. 
Full name of the lecturer

Stashulenok Sergei Pavlovich

6. 
Objectives of studying the discipline

Create a knowledge base of students in the field of probability theory and mathematical statistics acquaint students with the basic principles of probability theory and examples of their applications further formation of students’ skills in abstract mathematical thinking and the ability to apply it in specific tasks, enhancing their mathematical culture use the basic laws of random phenomena;

7. 
Prerequisites

Algebra,

8. 
Contents of the discipline

Theme 1. CONCEPT OF PROBABILITY Terminology of probability theory. The subject and problems of probability theory. Events, operations on events. Classical and geometric definitions of probability. The concept of Kolmogorov’s axiomatics. Probability properties. Examples of probability spaces. Classical, finite, discrete probability spaces. Geometric probability space, the Bertrand paradox. Statistical probability and frequency stability. Theme 2. INDEPENDENCE Conditional probability. Definition of conditional probability. Multiplication theorems. The formula of full probability and Bayesian formula. Independence of events. Determining the independence of two events and independence in the aggregate of several events. Independent testing. Bernoulli scheme Theme 3. RANDOM VALUES Random variables. Classification of random variables. Distributions: binomial, geometric, Poisson, uniform, normal, exponential, chisquare, Cauchy, etc. Function and density of distribution. The concept of independence of random variables. Mathematical expectation and variance, their properties. Inequalities of Chebyshev. Theme 4. Limit Theorems The concept of the law of large numbers and the central limit theorem (in the overview order). Theme 5. ELEMENTS OF MATHEMATICAL STATISTICS The subject and tasks of mathematical statistics. Basic concepts of the sampling theory: sample, variation series, histogram, frequency range, empirical distribution function.

9. 
Recommended literature

Main literature: 1. Borovkov AA Probability Theory. M .: Nauka, 1986. Additional literature: 12. Bolshev LN, Smirnov NV Tables of mathematical statistics. Moscow: Nauka, 1983. Collected problems on the discipline “Theory of Probability and Mathematical Statistics”: 21. Zhdanovich VF, Lazakovich NV Radyno N.Ya. Tasks for laboratory work on the course of probability theory and mathematical statistics in two parts. Part 1. Minsk, 1998. References: 28. Prokhorov Yu.V., Rozanov Yu.A. Probability theory. М .: Science, 1973

10. 
Teaching Methods

interactive methods of teaching (working in small groups (team), problem training) are organized taking into account the inclusion in the learning process of all students of the group. Joint activity means that each student makes his own individual contribution, in the course of the work there is an exchange of knowledge, ideas, methods of activity. Organized individual, steam and group work. Interactive methods are based on the principles of interaction, activity of trainees, reliance on group experience, mandatory feedback

11. 
Language of instruction

Russian

12. 
Conditions (requirements), routine monitoring

– testing;
– 
13. 
Appraisal Form

Exam
