Courses

Basic set theory concepts and operations. Random experiment, sample space, contingency, definitions of probability and basic properties. Addition theorem (Poincare's formula) and continuity theorem. Elements of combinatory analysis and probability theoretical applications. Restricted probability and stochastic independence. Multiplicative theorem, total probability theorem and Bayes' theorem. One-dimensional discrete and continuous random variables. Distribution function, probability function, probability density function. Special discrete and continuous distributions: Binomial, Geometric, Negative Binomial, Poisson, Uniform, Normal, Exponential, Gamma, Beta, Cauchy. Mean, variance, standard deviation, moments and other parameters of the distribution of random variables. In order to highlight the special elements of pedagogical and teaching competence contained in the course, emphasis is placed on its historical evolution, the development of its cognitive subject, as well as its applications in technology and/or other sciences.