Basic notions: probability, univariate and multivariate random variables. Marginal and conditional distributions.
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: most powerful test and uniformly most powerful test. Likelihood ratio tests.
Goodness of fit tests and independence test.
Some remarks on distribution-free tests on location parameters.