Probability theory and mathematical statistics

COURSE DESCRIPTION

The study course aims to learn basic questions about random events, random variables and elements of mathematical statistics. Several definitions of probability will be considered - classical, statistical and geometric. Random variables are divided into discrete and continuous random variables. The most important properties and characteristics of a random variable will be discussed. Mathematical statistics will look at how to calculate statistical indicators and solve other statistical problems using modern computer programs.

CONTENT

1. Random events. Basic concepts of probability theory. The random events and algebra of events. Definition of probability (classical, statistic, geometric). Addition and multiplication laws of probabilities. Conditional probability. Total probability and Bayes’ formula.Trials and Binomial probabilities
2. Random variable. Random variable (definition and classification). Functions of a random variable (distribution and density functions).  Discrete random variables. Expected value (mathematical expectation), variance and standard deviation of a discrete random variable; properties. The most important probability distributions of discreet random variables: uniform, hypergeometric, binomial, geometric, the Poisson distributions. Continuous random variable. Probability density function and distribution function. Expected value and variance. Characteristics of probability distribution. Chebyshev’s inequality.  The most important probability distributions of continuous random variables (exponential, uniform, normal, t-distribution). Strong law of large numbers. Central limit theorem and De Moivre-Laplace theorem.
Basic concepts of random variable probability distribution of discrete complete 2D
3. Mathematical statistics. Introduction to Statistic. Descriptive statistics (collecting and presentation of statistical data; cumulative sample distribution function). Inductive statistics (random sampling and sampling distributions).Point and interval estimation. Confidence interval
4. Basic concepts of correlation theory. Correlation coefficient.Linear regression equation