Infopaket

Probability theory

ОК.22

Обов’язкова дисципліна для ОП

First

2022/2023

4 Semester

6

Know and understand the basic definitions, formulas (in particular, formulas of full probability and Bayes), lemmas, theorems, models, concepts (in particular, the concepts of independence of events and conditional probability) and provisions of the discipline (in particular, the axiomatics of probability theory), the main characteristics of random variables and their properties; the main properties of Markov chain models with discrete and continuous time. Be able to perform calculations within the framework of finite and calculated probability schemes and in the conditions of the geometric probability model; construct and investigate probability distributions of discrete, continuous, singular and mixed random variables; check the dependence and independence of events and random variables. To justify one's own view on the problem, to communicate with colleagues on issues of formalization of problems and the choice of solution methods; make written reports.

Distance form

Know: the basics of mathematical analysis, discrete mathematics and algebra. Be able to: solve the simplest problems of mathematical analysis. Have basic skills in formalizing problems.

The discipline "Probability theory" has the following sections: Finite and calculated probability schemes. Geometric probability. Axiomatics of probability theory. Conditional probabilities. Discrete random variables. Independent random variables. Geneatrix Random variables (general case). Markov chains. Characteristic functions. The main task is to provide students with basic knowledge about random events and random variables; the ability to formalize and solve typical problems from the theory of probabilities, the skills of applying the acquired knowledge to applied problems. Discipline is a must. Uses concepts from mathematical analysis, discrete mathematics and algebra. Acts as a base for disciplines: actuarial mathematics, econometrics, financial mathematics, economic-mathematical modeling, decision-making methods. It is taught in the 4th semester, the volume is 180 hours. (6 ECTS credits), of which lectures – 44 hours, practical – 44 hours, independent work – 90 hours. There are 2 parts, 2 control papers and a test.

1. I. Gikhman, A. Skorokhod, M. Yadrenko "Probability theory and mathematical statistics". 2. A.V. Skorokhod "Elements of the theory of probabilities and the theory of random processes", K. 1975. 3. Lebedev E.O., Sharapov M.M. A course of lectures on probability theory. - K.: Norita-plus, 2007. - 168 p. 4. E.O. Lebedev, O.A. Chechelnytskyi, M.M. Sharapov, M.S. Bratiychuk Collection of problems on the theory of probabilities, KNU named after T. Shevchenko, 2006. Online program to check practical knowledge Index http://indexator.pp.ua All available author's methodical materials and electronic tables on the website http://teorver.pp.ua/ukr/ukr.php

Lecture, practical classes, independent work

Control work 1 and current evaluation (RN.1, RN.2): 30 points/15 points. Control work 2 and current evaluation (RN.1, RN.2): 30 points/15 points. Final assessment in the form of credit. It is issued based on the results of the students' work throughout the semester and does not provide for additional assessment measures for successful students. The student has the right to redo the test paper once with the possibility of receiving no more than 80% of the points assigned for the paper. The teacher determines the term of the revision.

Ukrainian