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Бакалавриат 2020/2021

## Теория вероятностей и математическая статистика

Статус:
Направление: 38.03.05. Бизнес-информатика
Когда читается: 2-й курс, 1, 2 модуль
Формат изучения: с онлайн-курсом
Охват аудитории: для своего кампуса
Язык: английский
Кредиты: 5

### Course Syllabus

#### Abstract

Probability Theory and Mathematical Statistics (PT&Stat below) is a core mathematical subject taught to the second year students in the 1st and 2nd academic modules. The material is split between probability theory and statistics almost evenly. The course covers classical probability topics from basic probability to limit theorems. More attention is paid to the conditional moments of multivariate random variables. Depending on the available time more advanced topics such as random walks, the Poisson process and Markov chains may be considered. The statistical section starts with the descriptive techniques but quickly switches to the inferential methods as they are more mathematically involved and require more eorts to explain. The topics covered here include sampling distributions, point and interval estimates, hypothesis testing. We conclude with a univariate and, if time permits, multivariate regression. Throughout the course a certain balance between mathematical rigor and clarity is maintained. Sometimes this dilemma is resolved in favor of illustrative examples which help students capture the main ideas and use them in practice rather than focus on blind memorizing the derivations. However, we nd it instructive to provide the tractable proofs whenever it makes pedagogical or some other sense. The course is taught in English and worth 5 credits.

#### Learning Objectives

• knows some of the basic ideas of theoretical statistics, emphasising the applications of these methods and the interpretation of tables and results.
• is familiar with concepts and methods that provide the foundation for more specialised courses in statistics

#### Expected Learning Outcomes

• have a grounding in probability theory and some grasp of the most common statistical methods;
• 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;
• recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions
• apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments;
• demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems
• 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
• 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
• 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
• explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform hypothesis tests in a number of different settings
• explain the principles of data reduction
• choose appropriate methods of inference to tackle real problems

#### Course Contents

• Axioms of probability
• Discrete random variables
• Jointly distributed random variable
• Conditional probability and independence
• Continuous random variables
• Limit theorems
• Methods of descriptive statistics
• Ideas of sampling and sampling distributions
• Point and interval estimates
• Hypothesis testing
• Linear regression models

• Exam
• MidTerm
• Homeworks
• Quizzes

#### Interim Assessment

• Interim assessment (2 module)
0.45 * Exam + 0.2 * Homeworks + 0.3 * MidTerm + 0.05 * Quizzes

#### Recommended Core Bibliography

• Probability and random processes, Grimmett, G. R., Stirzaker, D. R., 2004
• Probability and random processes, Grimmett, G. R., Stirzaker, D. R., 2009
• Statistical inference, Casella, G., Berger, R. L., 2002
• Statistical inference, Casella, G., Berger, R. L., 2002
• Statistics for business and economics, Newbold, P., Carlson, W. L., 2013
• Statistics, Freedman, D., Pisani, R., 1998