Contents of the discipline
Section 1. PROBABILISTIC SPACES
Topic 1.1. Introduction.
Topic 1.2. Terminology of probability theory. The subject and problems of probability theory. Events, operations on events.
Topic 1.3. Axiomatics of Kolmogorov. Probability properties.
Topic 1.4. Examples of probability spaces. Classical, finite, discrete probability spaces. Geometric probability space, the Bertrand paradox. Statistical probability and frequency stability.
SECTION 2. INDEPENDENCE.
Topic 2.1. Conditional probability. Definition of conditional probability. Multiplication theorems. The formula of full probability and Bayesian formula.
Topic 2.2. Independence of events. Determining the independence of two events and independence in the aggregate of several events. Independence of event classes.
Topic 2.3. Independent testing. Bernoulli scheme, polynomial scheme.
Topic 2.4. Limit theorems in the Bernoulli scheme. Local and integral limit theorems of Moivre-Laplace and Poisson and their applications.
Section 3. RANDOM VALUES.
Topic 3.1. Random variables and their distributions. Probability distribution as a measure on a Borel sigma algebra associated with a given random variable.
Topic 3.2. Classification of random variables. Lebesgue’s theorem. Distributions: binomial, geometric, Poisson, uniform, normal, exponential, chi-square, Student, Fisher, Cauchy, etc. Function and density of distribution.
Topic 3.3. Multidimensional random variables. Properties of the multidimensional distribution function. Classification of multidimensional random variables.
Topic 3.4. Independence of random variables. Criteria of independence.
Theme 3.5. Functional transformations of random variables. Functions of random variables and the corresponding transformations of the function and the distribution density. The convolution formula.
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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.
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.