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Course, academic year 2022/2023
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Probabilistic Methods - NMAI060
Title: Pravděpodobnostní metody
Guaranteed by: Department of Software Engineering (32-KSI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022 to 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Jaromír Antoch, CSc.
doc. RNDr. Ivan Mizera, CSc.
Class: Informatika Mgr. - Teoretická informatika
Informatika Mgr. - Softwarové systémy
Informatika Mgr. - Matematická lingvistika
Classification: Mathematics > Probability and Statistics
Is interchangeable with: NMAI016
Annotation -
Last update: T_KSI (15.04.2003)
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.
Aim of the course -
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)

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.

Course completion requirements -
Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Written exam.

Literature - Czech
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)

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.

Teaching methods -
Last update: G_M (29.05.2008)


Requirements to the exam -
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)

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.

Syllabus -
Last update: doc. RNDr. Petr Hnětynka, Ph.D. (07.02.2019)

• 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

Entry requirements -
Last update: prof. RNDr. Jaromír Antoch, CSc. (04.06.2018)

Random variables and vectors and their characterizations; convergence in distribution and in probability; central limit theorem; conditional density and conditional expectation; linear differencial equations.

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