Review of probability and basic univariate distributions.

Bivariate and multivariate distributions.

Transformations.

Moments, generating functions and inequalities.

Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.

Univariate, bivariate and multivariate normal distributions.

Proof of the central limit theorem.

Distributions associated with the normal distribution: Chi-square, t and F.

Application to normal linear models.

Theory of minimum variance unbiased estimation.