Discrete and continuous random variables, expectation of functions of random variables, joint distribution functions, independent random variables, moment generating functions, limit theorems, conditional probability and conditional expectation, the exponential
distribution, definition of stochastic processes, the Poisson process, simulating discrete and continuous random variables, simulating stochastic processes, Markov chains, ChapmanKolmogorov equations, classification of states, limiting probabilities, mean time spent in
transient states.

 After the completion of the course, the students:

• will know the basic categories of mathematical and probabilistic tools, which are used for the solution of problems with elements of uncertainty or randomness.
• will know the notion of stochastic process and will be familiar with the basic categories, as Poisson processes and Markov chains
• will be capable to cope with courses in other semesters, which base their theory on stochastic processes

 Not required.

 Notes of the tutor.

Lectures, resolving exercises, Laboratory Exercises.

 Systematic development and explanation of the theory, methods of solutions of exercises

 Face-to-face