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Differential equations and Probability theory. Part two “ Probability theory”

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Обов’язкова дисципліна для ОП

First

2022/2023

4 Semester

2

The student have to know: the basic concepts of probability theory, basic probability distributions and their numerical characteristics, understand the idea of the basic theorems of probability theory - the law of large numbers and the central limit theorem, have an idea of ​​random process.

Full-time form

The course "Differential Equations and Probability Theory (Part 2)" is based on knowledge of the basic discipline "Mathematical Analysis" and knowledge of the first part of this course "Differential Equations".

Differential equations and probability theory (part 2 Probability theory) consists of two content modules №1 "Fundamentals of probability theory" and №2 "Distributions of random variables. Central Limit Theorem". The first of them discusses the probability space, conditional probability, the sequence of n independent experiments (Bernoulli process), the random variable and its distribution. The second module discusses the numerical characteristics of random variables, the law of large numbers, the central limit theorem, as well as some examples of random processes.

1. Гнєденко Б.В.Курс теорії ймовірностей. – К.: ВПЦ Київський університет, 2010. – 464 с. 2. Єфіменко С.В., Іваненко Д.О., Сугакова О.В. Методичний посібник з курсу «Теорія ймовірностей» – К.: Видавнича лабораторія факультету радіофізики, електроніки і комп’ютерних систем КНУ імені Тараса Шевченка, 2018. – 100 с. 3. Карташов М.В. Імовiрнiсть, процеси, статистика : Посiбник. – К.: Видавничополiграфiчний центр ’Київський унiверситет’, 2008.– 494 с. 4. Теорія ймовірностей: Збірник задач/ за ред. А.В. Скорохода. – К.: Вища школа, 1976. – 384 с. 5. Гихман И.И., Скороход А.В., Ядренко М.И. Теория вероятностей и математическая статистика. – К.: Вища школа, 1979. – 408 с.

Lectures in the amount of 16 hours and seminars in the amount of 14 hours.

Semester score: The discipline has two modules, each of which is estimating at 30 points. Final score (exam): the form of the exam is written-oral. The test paper consists of 2 theoretical questions (10 points each) and two (10 points each). In total, you can get from 0 to 40 points for the exam. The condition for achieving a positive grade for the discipline is to obtain at least 60 points, the exam score can not be less than 24 points.

Ukrainian