Probability theory and mathematical statistics

Objectives: An introduction to probability and mathematical statistics, discussion of basic concepts, developing problem-solving skills; it provides an insight into practical applications.

Course material: Probability, statistics and inference. Probability model. Conditional probability, independent events. Random variables and their characteristics. Specific discrete and continuous distributions. Functions of random variables. Laws of large numbers. The central limit theorem. Elements and concepts of (mathematical) statistics.  Confidence intervals. Hypothesis testing methods. Hypotheses concerning the parameters of the normal variable. Non-parametric tests. Correlation and regression.