1. Continuous and discrete random variable (vector), probability function, density function. Probability. 2. Properties of probability. Cumulative distribution and its properties. 3. Relationships between probability, density and cumulative distributions of random variable. Marginal random vector and its distribution. 4. Independent random variables. Numeric characteristics of random variable: mean and variance, quantiles. Rules of calculation mean and variance. 5. Numeric characteristics of random vectors: covariance, correlation coefficient. Normal distribution - definition, using. 6. Chi-square distribution, Student´s distribution. Random sampling, sample statistics. 7. Point estimation of distribution parameters, desirable properties of an estimator - definition, interpretation. 8. Confidence interval for distribution parameters. 9. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters. 10. Goodness-of-fit tests.

1. Empirical distributions. Histogram. Probability and density distributions. 2. Probability. Cumulative distribution. 3. Relationships between probability, density and cumulative distributions. 4. Transformation of random variable. 5. Calculation of mean, variance and quantiles of random variable. Calculation rules of mean and variance. 6. Correlation coefficient. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson. 7. Calculation of probability for normal distribution. Work with statistical tables. Calculation of point estimators. 8. Confidence interval for normal distribution parameters. 9. Tests of hypotheses for normal distribution parameters. 10. Goodness-of-fit tests.