Learning outcomes
After passing the course a student
· knows design of modern probability theory;
· knows the concept of random variables and some most common probability distributions and is able to compute various numerical parameters related to both discrete and continuous random variables;
· knows basic methods of estimation and testing theory;
· understands the entity of the estimate and are able to characterize it by the corresponding properties (unbiasedness, efficiency, consistency);
· knows the basic methods for deriving estimates and are able to apply them (the maximum likelihood, least-squares methods and the method of moments);
· understand the entity of the hypothesis and are able to construct them in different situations;
· is able to construct interval estimates and handle non-normal data;
· has received training in mathematical statistics that is appropriate for studying field related advanced statistical methods.
Brief description of content
In the part of probability theory, the random events and properties of classical probability are considered. The course covers the theory of random variables and their distributions. In the part of mathematical statistics, the course covers basics of the statistical inference. First, a point estimator, its properties, and methods for finding it are considered. Also, the interval estimation and testing of statistical hypotheses are treated.
