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Probability theory and mathematical statistics

ОК 27.

Обов’язкова дисципліна для ОП

First

2023/2024

4 Semester

4

Learning outcomes are knowledge of the fundamental laws of probability theory and mathematical statistics, basic distributions of random variables and their numerical characteristics, the law of large numbers and central limit theorems, statistical estimates of parameters of random variable distributions. Also, the result is the development of methods for obtaining, experimental research and theoretical description of problems of probability theory and mathematical statistics, in particular, the ability of students to apply knowledge in practical situations for empirical estimates of mathematical expectation and variance of random variables.

Full-time form

Know the basic concepts of combinatorics such as permutations, placements, combinations (compounds); basic concepts of set theory, such as set, element set, subset, empty and universal set, power set. Be able to perform operations on sets such as union, intersection, difference, addition; be able to find the boundary of a function at a point, calculate derivatives and integrals, decompose a function into a power series. Have the skills to calculate double and improper integrals, differentiation under the sign of the integral, elementary methods of summation of series, concepts and methods of theory of functions of a complex variable.

The normative discipline "Probability Theory and Mathematical Statistics" is a component of the cycle of professional training of specialists of educational and qualification level "Bachelor of Physics" and basic for the study of all physical and mathematical disciplines. The course program is aimed at students who are already familiar with mathematical analysis, differential calculus. Learning outcomes are knowledge of the fundamental laws of probability theory and mathematical statistics, basic distributions of random variables and their numerical characteristics, the law of large numbers and central limit theorems, statistical estimates of parameters of random variable distributions. Teaching methods: lectures, consultations, practical classes. Assessment methods: surveys in the course of practical classes, modular tests after the main sections of the course and credit (4 semester). The final grade consists of intermediate grades (semester grade 80%) and credit (20%).

4. Yezhov SM, Probability Theory, Mathematical Statistics and Random Processes. Tutorial. - Kyiv, University of Kyiv, 2001. 9. O.M. Radchenko, Basics of probability theory. Tutorial. - K., Kyiv University, 2007. - 99 p

The total amount of 120 hours, including: Lectures - 30 hours. Practical classes - 30 hours. Independent work - 60 hours.

The control is carried out according to the module-rating system, which consists of 2 content modules. The knowledge assessment system includes current and modular knowledge control. Forms of current control: assessment of homework and modular tests performed by students during practical classes. The student can receive a maximum of 80 points for homework, independent assignments, oral answers, additions to practical classes, modular tests and 20 points in the test. Modular control: 2 modular control works. The student can receive a maximum of 70 points for modular tests. The final semester control is conducted in the form of a test (20 points) in the fourth semester. The test includes 1 theoretical questions (5 points) and 5 tasks (15 points). A credit test is not required if the student received more than 60 points during the semester assessment.

Ukrainian