Probability Theory and Mathematical Statistics

2026/2027

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Mathematics

Course type:

Compulsory course

When:

2 year, 1, 2 module

Instructors

Grinikh, Alexandra

Pankratova, Yaroslavna

Course Syllabus

Abstract

The goal of studying the discipline is learning the methods of computation of probabilities of random events and probability distributions of random variables, solving statistical estimation problems, notions of the theory of statistical hypotheses testing, that allow the student to apply this knowledge in the disciplines such as “Methods of Optimal Solution”, “Mathematical Models in Economics”, “Game Theory”, “Econometrics”. The course “Probability Theory and Mathematical Statistics” will be used in the theory and applications of multidimensional statistical analysis, mathematical economics, econometrics. The material of the course can be used for development and application of numerical methods of solving problems in various regions sciences and for creating and studying mathematical models of such problems.

Learning Objectives

• The goal of studying the discipline is learning the methods of computation of probabilities of random events and probability distributions of random variables, solving statistical estimation problems, notions of the theory of statistical hypotheses testing, that allow the student to apply this knowledge in the disciplines such as “Methods of Optimal Solution”, “Mathematical Models in Economics”, “Game Theory”, “Econometrics”. The course “Probability Theory and Mathematical Statistics” will be used in the theory and applications of multidimensional statistical analysis, mathematical economics, econometrics. The material of the course can be used for development and application of numerical methods of solving problems in various regions sciences and for creating and studying mathematical models of such problems.

Expected Learning Outcomes

• the student can define the relevant sample space, compute the probabilities of random
• can solve problems about random variables and their characteristics
• can use Chebyshev inequality and Markov inequality
• can compute sample characteristics, construct the empirical distribution function, histogram and the frequency polygon
• can solve problems about construction of confidence intervals for the parameters of the normal sistribution, test the hypothesis about the mean for samples from the normal distribution
• can find the estimates of the parameters of the distribution
• can test parametric and nonparametric hypotheses
• can solve problems about two dimensional random variables and their charactersitics

Course Contents

• 1. Events and Bernoulli trials
• 2. One dimensional random variables
• 3. Law of Large Numbers and Central Limit Theorem
• 4. Two dimensional random variables.
• 5. Basic notions of mathematical statistics
• 6. Samples from normal distribution
• 7. Statistical hypotheses testing
• 8. Statistical theory of parameter estimation

Assessment Elements

• Test 1
• Test 2
• Exam
• Test 3
• In class work
  Под активностью понимается: посещаемость, работа на семинарах, выход к доске с решением задач.

Interim Assessment

• 2026/2027 2nd module
  0.14 * Test 3 + 0.14 * Test 2 + 0.07 * In class work + 0.14 * Test 1 + 0.44 * Exam

Bibliography

Recommended Core Bibliography

• Marcelo Sampaio de Alencar, & Raphael Tavares de Alencar. (2016). Probability Theory. Momentum Press.

Recommended Additional Bibliography

• 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

Authors

• Podkopaev Oleg Borisovich
• Brodskaia Natalia Nikolaevna