Probability Theory and Mathematical Statistics

Major: Philology (Applied Linguistics)
Code of subject: 6.035.10.O.023
Credits: 6.00
Department: Mathematics
Lecturer: Oryshchyn O.G., Klapchuk M.I.
Semester: 3 семестр
Mode of study: денна
Learning outcomes: 1. Solve problems using classical and geometric definition of probability. 2. Solve problems using conditional probabilities, the formula for multiplying probabilities, the formula for total probability, the Bayes' formula. Check events for independence, non-independence, find the probabilities of independent events. 3. Using the formula of the Bernoulli scheme and the asymptotic formulas in the Bernoulli scheme, find the probabilities of events in the scheme of independent experiments. 4. Find the numerical characteristics of random variables, the distribution of the function of a random variable. 5. Find the numerical characteristics of random vectors. 6. Find the mean, the correlation function of a random function, the mean and the correlation function from the derivative and the integral of a random function. 7. Master the basic facts and methods of mathematical statistics.
Required prior and related subjects: Algebra and analysis Discrete Math
Summary of the subject: The course "Probability Theory and Mathematical Statistics" consists of sections: "Random variables", "One-Dimensional Random Variables", "Multiple Random Variables", "Law of Large Numbers" and "Elements of Mathematical Statistics".
Assessment methods and criteria: Diagnosis of students' knowledge is carried out with the help of questioning in practical classes, tests and individual work.
Recommended books: 1. Drohomyretska HT etc. Probability Theory and Mathematical Statistics. - Lviv: Lviv Polytechnic Publishing House, 2013. - 396 p. (in Ukrainian). 2. Bobik OI, Beregova GI, Kopytko BI Probability Theory and Mathematical Statistics. - Kyiv: Publishing House "Professional", 2007. - 558 p.(in Ukrainian). 3. Hwei P. Hsu Theory and Problems of Probability, Random Variables, and Random Processes, McGraw-Hill, 1996.