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Бакалавриат 2022/2023

# Теория вероятностей и математическая статистика

Статус: Курс обязательный (Международный бизнес)
Направление: 38.03.02. Менеджмент
Когда читается: 1-й курс, 3 модуль
Формат изучения: без онлайн-курса
Охват аудитории: для своего кампуса
Язык: английский
Кредиты: 3
Контактные часы: 48

### Course Syllabus

#### Abstract

Probability Theory and Statistics is a one-module course, its main objective is to provide students with a foundation of probability and basic methods of statistical data analysis. The course introduces the learner to the concepts of random events, conditional events, discrete and continuous random variables, their basic characteristics (expectation, variance, covariance, etc.), Central Limit Theorem, fundamentals of statistics and statistical theory, point and interval parameter estimation, hypothesis testing. The study of the course is based on the following disciplines: the school course of mathematics (including the Probability Theory section) and the course of Higher Mathematics, studied in the first year.

#### Learning Objectives

• The goal of this course is to provide students with foundations of probability theory and basic methods of statistical data analysis

#### Expected Learning Outcomes

• Students know how to solve problems related with probability, recognize probability distribution, and find its characteristics
• Students are able to apply basic probabilistic formulas: the formula of total probability, Bayes’ formula
• Students are able to apply the Law of Large Numbers and the Central Limit Theorem
• Students are able to compute probabilities for continuous random variables, their expectations, variance, covariance
• Students are able to explain basic concepts of probability theory: random outcomes, random events, conditional probability, and independent random events
• A student can distinguish between a population and a sample
• A student is able to compute basic point estimates of population mean and population variance
• A student is able to construct confidence intervals for population mean, population proportion, or population variance
• A student is able to explain the concepts of a null hypothesis and an alternative hypothesis, type 1 and type 2 errors

#### Course Contents

• Probability Theory
• Mathematical Statistics

#### Assessment Elements

• Seminar activity
Seminar activity includes: attendance, homeworks, and class activity. All three components have equal weight
• Quizzes
• Test
• Exam

#### Interim Assessment

• 2022/2023 3rd module
0.15 * Quizzes + 0.4 * Exam + 0.3 * Test + 0.15 * Seminar activity

#### Recommended Core Bibliography

• Modern mathematical statistics with applications, Devore, J. L., 2007
• Statistics for business and economics, Newbold, P., 2007

#### Recommended Additional Bibliography

• Прикладные методы анализа статистических данных : Учеб. пособие, Горяинова, Е.Р., 2012
• Теория вероятностей и математическая статистика. Базовый курс с примерами и задачами, учебное пособие, под ред. А. И. Кибзуна, 224 с., Кибзун, А. И., Горяинова, Е. Р., Наумов, А. В., Сиротин, А. Н., 2002