# Mathematical Statistics, Basic Course

## Official Course Description

## Description

The course contain both probability and statistics. It starts with the basic concepts axioms of probability, conditional probability, and independent events. We then treat: Stochastic variables in one and several dimensions and functions of these. Expectation, variance, and covariance. Normal distribution, binomial distribution, Poisson distribution and other important distributions for measurements and frequencies. Conditional distributions and conditional expectations. Sums and linear combination of random variables. The law of large numbers and the central limit theorem. Descriptive statistics. Point estimates and their properties. Maximum likelihood and Least squares. Principles of interval estimates and hypothesis testing. Methods for normally distributed observations. Approximative methods based on the normal distribution. Correlation. Linear univariate and multiple regression, polynomial regression. Analysis of variance. Distribution free methods. Permutation test.