THE THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS

Abstract of the academic discipline

The purpose of studying the discipline: to master the basics of probability theory, to develop probabilistic-statistical thinking and intuition, to form the skills of building probabilistic research models and solving relevant problems, as well as the formation of future specialists in full-fledged theoretical knowledge and practical skills in the application of probabilistic-statistical methods for evaluation stochastic processes.
Practical significance and use of acquired knowledge. To acquaint students with basic concepts, methods, theorems and formulas of probability theory and mathematical statistics. To help acquire the skills of applying theoretical material in practice, to form the ability to conduct complex statistical analysis of mathematical models describing real phenomena and processes. To promote the development of those personal qualities that are of personal professional importance for the future bachelor in the context of integration into the European educational space.

Main learning outcomes
PRN#1. Apply knowledge of the basic forms and laws of abstract and logical thinking, the basics of the methodology of scientific knowledge, forms and methods of extracting, analyzing, processing and synthesizing information in the subject area of computer science.
PRN#3. To use knowledge of regularities of random phenomena, their properties and operations on them, models of random processes and modern software environments to solve problems of statistical data processing and build predictive models.

Subjects and types of educational classes
1 week
Lecture #1. 
"Subject and methods of probability theory."
Implementation of the Calculation-Graphic Work. Choice of option. 
Completion of task 1 of part 1-Probability theory.
2 week
Lecture #2. 
"Independence of random events."
Practical lesson #1. 
"Events and probability."
Implementation of the Calculation-Graphic Work. 
Completion of task 2 part 1-Probability theory.
3 week
Lecture #3. 
"Sequence of homogeneous independent trials."
Implementation of the Calculation-Graphic Work. 
Completion of task 3 part 1-Probability theory.
4 week
Lecture #4. "Discrete random variables".
Practical lesson #2. 
"Theorems about the probabilities of complex events."
Implementation of the Calculation-Graphic Work. 
Completion of task 4 of part 1-Probability theory.

5 week
Lecture 5. "Probability distributions and numerical characteristics of discrete random variables."
Implementation of the Calculation-Graphic Work.
 Completion of tasks 5 part 1-Probability theory.

6 week
Lecture #6. 
"Continuous random variables."
Practical lesson #3. 
"Sequence of independent tests (Bernoulli scheme)".
Implementation of the Calculation-Graphic Work. Completion of tasks 5 part 1-Probability theory.
7 week
Lecture #7. 
"Distribution functions and numerical characteristics of continuous random variables."
Implementation of the Calculation-Graphic Work. 
Completion of task 6 of part 1-Probability theory.
8 week
Lecture #8. 
"Important laws of the distribution of continuous random variables."
Practical lesson #4. 
"Discrete random variables".
Modular control work #1.
Implementation of the Calculation-Graphic Work. Protection of 1 part.
9 week
Lecture #9. 
"Important distributions in statistics."
Implementation of the Calculation-Graphic Work. 
Completion of task 7 of part 2 – Mathematical statistics
10 week
Lecture #10. 
"Typical problems of mathematical statistics."
Practical lesson #5. 
"Continuous random variables".
Implementation of the Calculation-Graphic Work. 
Completion of task 8 of part 2 – Mathematical statistics
11 week
Lecture #11. 
"Graphic presentation of statistical data."
Implementation of the Calculation-Graphic Work. 
Completion of task 9 of part 2 – Mathematical statistics
12 week
Lecture #12. 
"Statistical evaluation of parameters of distributions, part 1."
Practical lesson #6. 
"Sampling method".
Implementation of the Calculation-Graphic Work. 
Completion of task 10 part 2 - Mathematical statistics
13 week
Lecture #13. "Interval evaluations".
Implementation of RGR. Completion of task 11 of part 2 – Mathematical statistics
14 week
Lecture #14. "Statistical hypotheses."
Practical lesson #7. 
"Interval evaluations".
Implementation of the Calculation-Graphic Work.
 Completion of task 12 part 2 - Mathematical statistics
15 week
Lecture #15. 
"Testing hypotheses about the type of distribution."
Modular control work #2.
Implementation of the Calculation-Graphic Work. 
Defense of 2 part.

Individual work of the applicant takes place during the semester and consists of preparation for classroom classes, control measures.
Consultations: are carried out by the teacher during the semester according to the schedule.

Assessment of learning outcomes
The evaluation of the results of studies in the discipline is carried out according to the cumulative system, which allows the student to receive a maximum of 100 points during the semester.
Module #1
Practical lessons - maximum points per lesson.
Modular test 1 – perfect performance –20 points (in each task of the modular test
Calculation and graphic work (Part 1). Evaluation for performance - 10 points. The term of provision and protection –8 week.
Module #2
Practical lessons 5, 6 - maximum of 7 points per lesson, practical lesson 7 – maximum of 6 points per lesson.
Calculation and graphic work (Part 2). Evaluation for performance - 10 points. The term of provision and protection – 15 week.
Modular test 2 – perfect execution of– 20 points (in each task of the modular test, the maximum number of points for each task is given).

Links to recommended sources of information
1.Барковський В.В. Теорія ймовірностей та математична статистика / В.В. Барковський, Н.В. Барковська,  О.К. Лопатін. - Київ : ЦУЛ, 2002. - 448 с. 
2. Бобик О.І. Теорія ймовірностей і математична статистика: підручник / О.І. Бобик, Г.І. Берегова, Б.І. Копитко. - К.:ВД «Професіонал», 2007. - 560 с.       
3. Жалдак М.І. Теорія ймовірностей і математична статистика: підручник . − Вид. 2, перероб. і доп. / М.І. Жалдак, Н.М. Кузьміна, Г.О. Михалін. − Полтава : "Довкілля-К", 2009. − 500 с. 
4.Зайцев Є. П. Теорія ймовірностей і математична статистика. Базовий курс з індивідуальними завданнями і розв’язком типових варіантів : навч. посібн. / Є. П. Зайцев. – 2-ге видання, стереотипне. – К.: Алерта, 2017. – 440 с.
5. Кармелюк Г. І. Теорія ймовірностей та математична статистика. Посібник з розв'язування задач : Навч. посібник. - К.: Центр учбової літератури, 2007 - 576 с.
6. Сеньо П. С. Теорія ймовірностей та математична статистика : підручник. - Київ : Знання, 2007. - 556 c.