Infopaket

Probability theory and mathematical statistics

ОК 28

Обов’язкова дисципліна для ОП

First

2024/2025

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%).

1. Turchyn V.M. Probability theory and mathematical statistics. Basic concepts, examples, problems: Textbook for students of higher educational institutions. – Dnipropetrovsk: IMA-press, 2014. – 556 p. 2. Slyusarchuk P.V. Probability theory and mathematical statistics. – Uzhgorod: Publishing house “Karpaty” 2005. - 178 p. 3. Gnedenko, B. V. Course of probability theory: textbook / B. V. Gnedenko – K.: Publishing and printing center "Kyiv University", 2010. – 464 p. 4. Yezhov S. M. Problems in probability theory and mathematical statistics: solution methods: teaching and methodological manual / S. M. Yezhov, L. V. Shmelyova. – K. : Publishing and Printing Center "Kyiv University", 2013. – 172 p. 5. Radchenko O.M., Fundamentals of Probability Theory. Textbook. - K., Kyiv University, 2007. - 99 p.

The total amount of 90 hours, including: Lectures - 15 hours. Practical classes - 30 hours. Independent work - 45 hours.

Control is carried out according to the modular rating system, which consists of 3 content modules. The knowledge assessment system includes current and modular knowledge control. The results of students' educational activities are assessed on a 100-point scale. Forms of current control: evaluation of homework, tests and modular tests performed by students during practical classes. A student can receive a maximum of 70 points for completing homework, independent tasks, oral answers, additions in practical classes, modular tests, 10 points for a project and 20 points for a test. Modular control: 2 modular tests and a report. A student can receive a maximum of 35 points for modular tests. Final semester control is carried out in the form of a test (20 points) in the fourth semester. The test task includes 5 theoretical questions (10 points) and 5 problems (10 points).

Ukrainian