Syllabus
• Discrete and continuous random variables and their characteristics.
• Recurrent events, their classification and applications.
• Markov chains with discrete states and discrete time, classification of states, stationary distribution, etc.
• Exponential distribution, its properties and applications
• Markov processes with discrete states and continuous time.
• Models of birth and death.
• Basics of theory of queues, modeling of serving networks.
• Poisson process and its applications.
• Durbin-Watson branching process and its applications
• Simulation of random objects studied during the lecture
Annotation
The main aim is to enlarge the basic knowledge from the course Probability and statistics. Attention will be paid especially to problems and applications of Markov chains, theory of queues, reliability theory and theory of information.