|
|
|
||
|
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.
Last update: T_KSI (15.04.2003)
|
|
||
|
The students will become familiar with the basics of the Markov chains, birth and death processes, queueing models and stochastic processes. They will be capable to understand stochastic approaches to the modelling of real random events of this nature.
Last update: Mizera Ivan, prof. RNDr., CSc. (05.10.2022)
|
|
||
|
Oral exam. Last update: Zichová Jitka, RNDr., Dr. (13.05.2023)
|
|
||
|
Prášková Z. a P. Lachout, Základy náhodných procesů, Karolinum, Praha 1998.
Feller W., An introduction to probability theory and its applications, Wiley, New York 1970.
Ross, S.M. Introduction to Probability Models. Academic Press, Elsevier, 2007.
Lawler, G. F., Introduction to Stochastic Processes, Second Edition. Chapman and Hall/CRC, Boca Raton, 2006. Last update: Mizera Ivan, prof. RNDr., CSc. (05.10.2022)
|
|
||
|
Lecture. Last update: G_M (29.05.2008)
|
|
||
|
The written examination will cover the material given by the syllabus within the scope presented during the lecture. It will consist of several problems having either the nature of the problems and exercises presented in the lecture, or also that of some simple elementary derivations (proofs) of suitable theoretical results. Students are supposed to know all fundamental definitions and theorems (including the assumptions), to the extent that they should be able to derive their simple consequences and address real problems with their help. Last update: Mizera Ivan, prof. RNDr., CSc. (05.10.2022)
|
|
||
|
• 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 Last update: Hnětynka Petr, doc. RNDr., Ph.D. (07.02.2019)
|
|
||
|
Random variables and vectors and their characterizations; convergence in distribution and in probability; central limit theorem; conditional density and conditional expectation; linear differencial equations. Last update: Antoch Jaromír, prof. RNDr., CSc. (04.06.2018)
|