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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 2016
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0 Ex [hours/week]
Capacity:	unlimited
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time

Guarantor:	prof. RNDr. Jaromír Antoch, CSc.
Class:	Informatika Mgr. - Teoretická informatika Informatika Mgr. - Softwarové systémy Informatika Mgr. - Matematická lingvistika
Classification:	Mathematics > Probability and Statistics

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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: G_M (05.06.2008)

The students will acquaint with the basics of the Markov chains, birth and death processes, queueing models and stochastic processes. They will be able to undestand stochstic approach to the modelling of real random events in this domain.

Course completion requirements -

Last update: RNDr. Jitka Zichová, Dr. (10.05.2018)

Oral exam.

Literature - Czech

Last update: prof. RNDr. Jaromír Antoch, CSc. (05.10.2018)

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.

Teaching methods -

Last update: G_M (29.05.2008)

Lecture.

Requirements to the exam -

Last update: prof. RNDr. Jaromír Antoch, CSc. (05.10.2018)

Examination is oral within a framework of discussed matter given by the syllabus a scope presented during the lecture. TODO It is necessary to know all fundamental definitions, theorems and assertions (including the assumptions), understand ther inter relations and be capable in outline explain their justification (proofs). Student should be able to analyze real problems.

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.