Basic elements of set theory. Random experiment, sample space, events, classical, frequentistic and axiomatic definition of probability. Basic properties of probability, Poincare’s formula and continuity theorem. Elements of combinatorial analysis and probabilistic applications. Conditional probability and stochastic independence. Multiplication rule, total probability theorem and Bayes rule. Univariate discrete and (absolutely) continuous random variables. Distribution function, probability mass function and probability density function. Special discrete and continuous distributions: Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Uniform, Normal, Exponential, Gamma, Beta, Cauchy. Expected value, variance, standard deviation, moments and other parameters of random variables.

In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences