Probability theory I* 1000-114bRP1*

Kolmogorov axioms.
Properties of probability measures. Borel-Cantelli lemma. Conditional probability. Bayes' theorem..
Basic probabilities: classical probability, discrete probability, geometric probability.

Random variables (one- and multidimensional), their distributions. Distribution functions.
Discrete and continuous distributions. Distribution densities. Parameters of distributions: mean value, variance, covariance. Chebyshev inequality.

Independence of: events, sigma-algebras, random variables. Bernoulli (binomial) process.
Poisson theorem. Distrubution of sums of independent random variables.

Convergence of random variables. Laws of large numbers: weak and strong. De Moivre-Laplace theorem.

The program is in principle the same as for the basic lecture. However, topics will be treated more deeply and often in a more general way. The lecture is addressed to students with deeper interest in the subject, eager to tackle related exercises and problems.