Infopaket

Probability theory and mathematical statistics

Обов’язкова дисципліна для ОП

First

2023/2024

4 Semester

11

Know and understand the basic definitions, formulas (including total probability and Bayesian formulas), lemmas, theorems, models, concepts (including the concept of event independence and conditional probability) and the position of the discipline (including axiomatics of probability theory), basic characteristics of random variables and their properties; main properties of Markov chain models with discrete and continuous time. Know and understand the basic formulas, models, concepts and problems of mathematical statistics. Be able to perform calculations within the finite and calculated probability schemes and in terms of the geometric probability model; build and investigate probability distributions of discrete, continuous, singular and mixed random variables; check the dependence and independence of events and random variables.

Full-time form

Know: basics of probability theory and mathematical statistics, mathematical analysis and algebra Be able to: apply knowledge of probability theory and mathematical statistics. Have basic skills: solve problems in probability theory. To access the discipline "Probability Theory and Mathematical Statistics" of the educational-professional program "Systems Analysis" the student must master the results of learning provided by the disciplines "Mathematical Analysis", "Algebra", "Discrete Mathematics". The discipline "Probability Theories and Mathematical Statistics" is the basis for mastering the disciplines "Mathematical Demography and Random Process Modeling", "Mathematical Insurance Models and Asymmetric Cryptography", "Customer Theory".

The discipline "Probability Theory and Mathematical Statistics" is part of the educational and professional training program for the first (bachelor's) level of higher education in the field of knowledge 12 "Information Technology" in 124 "System Analysis", educational and professional program "System Analysis". This course is a compulsory subject in the System Analysis program. It is taught in 4 and 5 semesters in the amount of 330 hours. (11 ECTS credits) in particular: lectures - 74 hours, practical - 74 hours, consultations - 8 hours, independent work - 174 hours. The course provides 4 content parts and 4 tests. The discipline ends with a test in the 4th semester and an exam in the 5th semester.

1. Victor Barkovsky, Nina Barkovskaya, Alexey Lopatin. Probability theory and mathematical statistics.- Center for Educational Literature. - 2019. - 424 p. 2. Vadym Radchenko, Oleksandr Borysenko, Yulia Mishura, Heorhiy Shevchenko. Collection of problems in financial mathematics. - Technology. - 2007. - 256p. 3. Gichman, A. Skorokhod, M. Yadrenko "Probability theory and mathematical statistics". 4.А.В. Skorokhod "Elements of probability theory and the theory of random processes", K. 1975. 5.A. Dorogovtsev “Probability theory. Collection of problems ", K. 1980. 6. Lebedev EA, Sharapov MM Course of lectures on probability theory. - K .: Norita-plus, 2007. - 168 p. 7. EO Lebedev, OA Chechelnytsky, MM Sharapov, MS Bratiychuk Collection of problems in probability theory, KNU. T. Shevchenko, 2006.

Lecture, practical classes, independent work

Test work, exam

Ukrainian