Basic notions: probability, univariate and multivariate continuous and discrete random variables.
Properties of probability distributions (moments).
Convergence of sequences of random variables.
Law of large numbers. Central Limit Theorem.
Notion of population and sample.
Sample statistics and their distributions (mean, variance, difference of means, ratio of variances).
Estimators and their properties (methods of maximum likelihood, moments and minimum squared error).
Confidence intervals (mean, difference of means, variance).
Hypothesis testing: mean, difference of two means, variance. Analysis of variance.
Power function: most powerful tests and uniformly most powerful tests. Likelihood ratio tests.