SubjectsSubjects(version: 825)
Course, academic year 2017/2018
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Probabilistic Methods - NMAI060
Czech 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
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.

Literature - Czech
Last update: T_KSI (15.04.2003)

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.

Teaching methods -
Last update: G_M (29.05.2008)


Requirements to the exam -
Last update: prof. RNDr. Jaromír Antoch, CSc. (09.10.2017)

Exam is oral. It is examined what has been presented during the lecture.

Syllabus -
Last update: T_KSI (15.04.2003)

1. Discrete and continuous random variable and their characteristics. Random vectors and their characterizations.

2. Central limit theorem and its applications.

3. Markov chains, classification of states, stationary distribution.

4. Poisson process and its applications.

5. An introduction to the queues, birth - and - death models, queueing networks.

6. Exponential distribution and its use in the theory of reliability. Characteristics of reliability, time to failure, intensity of failures, reliability of complex systems.

7. Notion of information from the probabilistic and statistical point of view.

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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