1.       

Title of the discipline (basic disciplines)

ADDITIONAL CHAPTERS OF THE PROBABILITY THEORY

2.       

Course of Study

Course 4, specialty Mathematics (research and production activities)

3.       

Semester of training
(for each semester a separate table)

8

4.       

Amount of credits
(academic plan)

4

5.       

Full name of the lecturer

Stashulenok Sergei Pavlovich

6.       

Objectives of studying the discipline

To supplement the knowledge base and skills of students in the field of probability theory and mathematical statistics, in-depth 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, increasing their mathematical culture.
As a result of studying the discipline, the student must:
know:
 concepts of probability theory and mathematical statistics;-
 mathematical models of random phenomena;-
 limit theorems of probability theory;-
be able to:
 use the basic laws of random phenomena;-

7.       

Prerequisites

Algebra and number theory,
Discrete Math,
Analytic geometry,
Mathematical analysis,
Differential equations,
The theory of functions of a complex variable,
Functional analysis and integral equations,
Theory of probability and mathematical statistics

8.       

Contents of the discipline

Section 1. BASICS OF THE THEORY OF RANDOM PROCESSES.
Topic 1.1. Definition of a random process. Processes with discrete and continuous time. The trajectories of a random process.
Topic 1.2. Random processes with independent increments. Examples: a Poisson random process and a random process of Brownian motion.
Section 2. ELEMENTS OF MATHEMATICAL STATISTICS.
Topic 2.1. The subject and tasks of mathematical statistics.
Topic 2.2. Basic concepts of sampling theory: sampling, variational series, histogram, frequency range, empirical distribution function, Glivenko’s theorem. Asymptotic normality of sample moments.
Topic 2.3. Estimation of unknown parameters. Consistency (strong consistency) of evaluations. Displaced and unbiased estimates, optimal estimates. Inequality Rao-Kramer. Efficiency. Methods of maximum likelihood and moments. Sufficient statistics. Trust assessment.
Topic 2.4. Testing of statistical hypotheses. Evenly the most powerful criteria.
Topic 2.5. Parametric hypotheses. The Neumann-Pearson lemma. Examples.
Topic 2.6. Linear Regression and Least Squares.

9.       

Recommended literature

Main literature:

1. Borovkov AA Probability Theory. M .: Nauka, 1986.
2. Wentzel A.D. Course of the theory of random processes. – Moscow: Nauka, 1978.
3. Gikhman II, Skorokhod AV, Yadrenko MI Theory of Probability and Mathematical Statistics. Kiev: Vishcha Shk., 1979.
4. Gnedenko B. V. Course of the theory of probability. Moscow: Nauka, 1988.
5 Zuev M., Sechko Vl.  Probability Theory i mathematical statistics. Mozyr: White Wind 2000.6. Ivchenko GI, Medvedev Yu. I. Mathematical statistics. М.: Vysch. shk., 1984.
7. Lazakovich NV, Stashulenok SP, Yablonsky O.L. Theory of Probability: A Textbook. – 3rd ed., With modified. – Minsk: BSU, 2013.
8. Rozanov Yu. A. The theory of probability, random processes, mathematical statistics. Moscow: Nauka, 1985.
9. Sevastyanov BA Course of the theory of probability and mathematical statistics. Moscow: Nauka, 1982.
10. Chistyakov VP Course of the theory of probability. M .: Nauka, 1987.
11. Shiryaev AN Probability. M .: Nauka, 1989.

Additional literature:

12. Bolshev LN, Smirnov NV Tables of mathematical statistics. Moscow: Nauka, 1983.
13. AN Kolmogorov, Basic concepts of the theory of probability. Moscow: Nauka, 1974.
14. Kramer G. Mathematical methods of statistics. Moscow: The World, 1976.
15. VM Kruglov. Additional chapters of the theory of probability. М: Vysch. shk., 1984.
16. Lazakovich NV, Stashulenok SP, Yablonsky O.L. Course of probability theory: an electronic textbook. – Minsk: E-book of the Belarusian State University, 2003.
17. Leman E. Testing of statistical hypotheses. Moscow: Nauka, 1964.
18. Partasarati K. Introduction to probability theory and measure theory. Moscow: Mir, 1983.
19. Feller V. Introduction to the theory of probability and its applications. М .: Мир, 1984.Т.1,2.
20. PA Henneken and A. Tortra, Theory of Probability and some of its applications. Moscow: Nauka, 1974.

 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.
22. Zhdanovich VF, Lazakovich N.V. Radyno N.Ya., Stashulenok S.P. Tasks for laboratory work on the course of probability theory and mathematical statistics in two parts. Part 2. Minsk, 1999.
23. Meshalkin L.D. A collection of problems in probability theory. M: MSU, 1963.
24. Prokhorov AV, Ushakov VG, Ushakov NG Problems on the theory of probability: Basic concepts. Limit theorems. Random processes. M: Science, 1986.
25. Sevastyanov BA, Chistyakov VP, Zubkov AM Collection of problems in probability theory. M: Science, 1989.
26. Theory of Probability: a Workshop: Textbook. allowance for university students. specialist. : at 2 pm Part 1 / [aut .: NV Lazakovich, EM Radyno, SP Stashulenok, SL Shtin, O.L. Yablonsky]; Ed. NV Lazakovich. – Minsk: BSU, 2011. – 147 p.
27. Theory of Probability: a Workshop: Textbook. allowance for university students. specialist. : at 2 pm Part 2 / [aut .: NV Lazakovich, EM Radyno, SP Stashulenok, A. G. Yablonskaya, O.L. Yablonsky]; Ed. NV Lazakovich. – Minsk: BSU, 2014.- 175s.

References:

28. Prokhorov Yu.V., Rozanov Yu.A. Probability theory. М .: Science, 1973
29. A handbook on probability theory and mathematical statistics. Korolyuk VS, Portenko NI, Skorokhod AV, Turbin AF.  Moscow: Nauka, 1985.

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

– test;
– Colloquium
The offset is given taking into account:
30% – work in laboratory and practical classes, 70% – control work, colloquium

–

13.   

Appraisal Form

Offset