Theory of probability and mathematical statistics

Description: Probability theory is a mathematical science that uses probabilistic models to study random phenomena, different from deterministic approaches. Mathematical statistics, an important part of the theory, deals with methods of analyzing mass phenomena, where randomness plays a key role.

Amount of credits: 5

Пререквизиты:

• Mathematical Analysis 2

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• Study of basic concepts and mathematical methods for solving practical problems in probability theory and mathematical statistics

Objective

• -formation of concepts about the theory of probability and mathematical statistics, features of application in the process of solving professional problems;
• -mastering the skills of formulating mathematical statements of problems, finding a suitable method for solving them

Learning outcome: knowledge and understanding

• Knows the method of collecting and processing information; relevant sources of information in the field of professional activity; system analysis method
• Point estimation of parameters and determination of the confidence interval, the main methods of statistical processing

Learning outcome: applying knowledge and understanding

• knows how to use mathematical methods in technical applications, calculate the basic numerical characteristics of random variables, solve the main problems of mathematical statistics; solve typical calculation problems
• owns methods of mathematical analysis and modeling; methods for solving problems of analysis and calculation of the characteristics of physical systems, basic methods for processing experimental data, methods for working with applied software products

Learning outcome: formation of judgments

• Analyzes the effectiveness of the obtained model, applying mathematical methods and has an idea about mathematical models and methods for solving applied problems from various fields of natural science.

Learning outcome: communicative abilities

• Able to solve applied problems in a team using mathematical methods, to correctly defend his point of view, to propose new solutions

Learning outcome: learning skills or learning abilities

• Strive for professional and personal growth by mastering the techniques and skills for solving specific problems from different areas of the discipline, helping to further solve engineering, production and scientific problems

Teaching methods

Information and communication technology;

Technology for the development of critical thinking;

Integrated learning technology;

Traditional technologies (lectures, practical classes)

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Алгебра событий
• Элементы комбинаторики
• Теорема сложения вероятностей
• Формула полной вероятности
• Испытания с повторениями
• Случайные величины
• Числовые характеристики дискретной случайной величины
• Плотность распределения непрерывных случайных величин
• Равномерное, нормальное, показательное распределение непрерывных случайных величин и их числовые характеристики
• Начальные и центральные теоретические моменты случайных величин
• Многомерные случайные величины
• Элементы математической статистики
• Интервальные оценки
• Критерии и применение его для различных предполагаемых проверок
• Определение параметров линейной и нелинейной регрессии методом наименьших квадратов

Key reading

• Севастьянов Б. А. Курс теории вероятностей и математической статистики. — Москва-Ижевск: Институт компьютерных исследований, 2019
• Гмурман В.Е. Руководство к решению задач по теории вероятностей и математической статистике. – М.: Высшая школа, 2008.
• Горбиков С.П., Филатов Л.В. Лекции по теории вероятностей и математической статистике. [Текст]: учебное пособие для вузов./ Горбиков С.П., Филатов Л.В.; Нижегор. Гос. Архитектур.- строит. ун-т – Н.Новгород: ННГАСУ, 2011
• Вентцель Е.С. Теория вероятностей. – М.: Физматгиз, 2002.
• Гмурман В.Е. Введение в теорию вероятностей и математическую статистику. – М.: Высшая школа, 2008.
• Письменный Д.Т. Конспект лекций по теории вероятностей и математической статистике. – М.: Айрис-пресс, 2004.
• Кибзун А.И. и др. Теория вероятностей и математическая статистика. Базовый курс с примерами и задачами. – М.: Физматлит, 2002.
• Тыныбекова С.Д., Рахметуллина Ж.Т., Конырханова А.А.Теория вероятностей и математическая статистика в вопросах и задачах. – Усть-Каменогорск: ВКГТУ, 2011.
• Рябушко А.П., Бархатов В.В. и др. Индивидуальные задания по высшей математике. – Минск: Высшая школа, 2009. – Т. 4.