2024/2025
Теория вероятностей и математическая статистика
Статус:
Маго-лего
Когда читается:
3, 4 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
"Probability Theory and Mathematical Statistics" is an academic discipline, related to the mathematical cycle. Within the course, students will get acquainted with the theoretical foundations of modern probability theory and inferential statistics, their main results, and learn to solve standard problems in this area. The main provisions of the discipline can be used in the future when studying the following disciplines, for example: Machine learning; Information theory; Applied statistics in machine learning.
Learning Objectives
- To have a grounding in probability theory and some grasp of the most common statistical methods;
- To develop students' skills in mathematical thinking;
- To prepare students to study further sections in probability, statistics and/or related disciplines;
- To deliver the required foundation for tackling the practical applications of probability and statistics in data analysis and machine learning;
- To broad general cultural and philosophical horizons of students;
Expected Learning Outcomes
- Know the basic concepts of probability theory.
- Be able to use the concept of conditional probability, total probability, and independence of events.
- Understand the concept of a random variable.
- Know how to use the probability mass functions for calculating the basic characteristics of a discrete random variable (expected value, variance).
- Know and be able to use alternative ways of describing a continuous random variable - probability density function and cumulative distribution function.
- Know how to calculate basic characteristics of a continuous random variable.
- Be aware of commonly used continuous distributions.
- Know how to work with a multivariate random variable using the joint probability distribution.
- Be able to detect the independent random variables, calculate the marginal distributions, covariance and correlation between the variables.
- Know the basic limit theorems of probability theory: the law of large numbers, the central limit theorem.
- Be able to derive and use the main sampling distributions - for mean, proportion and variance.
- Be able to estimate the main characteristics of a random variable by means of point or interval estimates.
- Know how to construct and interpret the confidence intervals for mean, proportion and variance.
- 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.
- Demonstrate an understanding that statistical techniques are based on assumptions and be able to apply correct assumptions for the given problems.
- Be able to use simple linear regression and correlation analysis.
Course Contents
- Introduction to probability. Probability space.
- Conditional probability, Total probability, Bayes’ theorem.
- Discrete random variables.
- Continuous random variables.
- Multivariate random variables.
- Limit theorems.
- Introduction to statistics. Sampling distribution. Point estimation of parameters.
- Confidence intervals.
- Testing of statistical hypotheses.
- Linear regression.
Interim Assessment
- 2024/2025 4th module0.3 * Exam + 0.3 * Home Assignments + 0.2 * Midterm + 0.2 * Quizzes
Bibliography
Recommended Core Bibliography
- An introduction to statistics : an active learning approach, Carlson, K. A., 2018
- Linde, W. (2017). Probability Theory : A First Course in Probability Theory and Statistics. [N.p.]: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1438416
- Курс теории вероятностей : учебник, Чистяков, В. П., 1987
Recommended Additional Bibliography
- Introduction to mathematical statistics, Hogg, R. V., 2014
- Ширяев, А. Н. Вероятность-1 : учебное пособие / А. Н. Ширяев. — Москва : МЦНМО, 2007. — 552 с. — ISBN 978-5-94057-105-6. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/9448 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
- Ширяев, А. Н. Вероятность-2 : учебное пособие / А. Н. Ширяев. — Москва : МЦНМО, 2007. — 416 с. — ISBN 978-5-94057-106-3. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/9449 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.