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# Probability Theory

2020/2021
Учебный год
ENG
Обучение ведется на английском языке
5
Кредиты
Статус:
Курс обязательный
Когда читается:
1-й курс, 2 модуль

### Course Syllabus

#### Abstract

Probability theory is the cornerstone of mathematical statistics and data analysis. In statistics, we assume that the analyzed data is obtained as a result of random experiments. For example, opinion poll results largely depend on the sample composition. If we want to make conclusions which can be extrapolated to other samples, first, we have to study the actual data generation process. We can do that by modelling this process using a system of random variables. In the Probability Theory course, we will begin with the basic notions of probability theory (conditional probability and independence) and then study discrete and continuous random variables and their properties. The law of large numbers and the central limit theorem are the key topics of this course. We also discuss how to study probabilistic processes using computer simulations.

#### Learning Objectives

• This course introduces some of the basic ideas of theoretical statistics, emphasizing the applications of these methods and the interpretation of tables and results.
• We will introduce concepts and methods that provide the foundation for more specialized courses in statistics.

#### Expected Learning Outcomes

• Students will be able to routinely apply a variety of methods for explaining, summarising, and presenting data and interpreting results clearly using appropriate diagrams, titles, and labels when required.
• Students will be able to summarise the ideas of randomness and variability and the way in which these link to probability theory to allow the systematic and logical collection of statistical techniques of great practical importance in many applied areas.
• Students will have a grounding in probability theory and some grasp of the most common statistical methods.
• Students will be able to recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions.
• Students will be able to perform inference to test the significance of common measures such as means and proportions and conduct chi-squared tests of contingency tables.
• Students will be able to use simple linear regression and correlation analysis and know when it is appropriate to do so.

#### Course Contents

• Data presentation.
• Elements of probability theory.
• Discrete random variables.
• Continuous random variables.
• Multivariate random variables.
• Conditional distributions.

#### Assessment Elements

• Quizzes
• Programming
• SGA
• Final Project

#### Interim Assessment

• Interim assessment (2 module)
0.2 * Final Project + 0.1 * Programming + 0.4 * Quizzes + 0.3 * SGA

#### Recommended Core Bibliography

• A course in probability theory, Chung, K. L., 2001