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Course, academic year 2023/2024
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Practical Course in Probability Methods - NMAI165
Title: Praktikum z pravděpodobnostních metod
Guaranteed by: Department of Software Engineering (32-KSI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:0/2, C [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Jaromír Antoch, CSc.
Class: Informatika Mgr. - volitelný
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: RNDr. Michal Kopecký, Ph.D. (12.05.2018)
The knowledge of ideas presented in the lecture NMAI060 Probability models will be deepened through solving more or less complicated problems with the eventual applications in the field of informatics. Basics of probability and knowledge obtained from the lecture is expected.
Aim of the course -
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)

Reinforcement of the concepts and ideas presented in the lecture NMAI060 Probability models through solving relevant problems.

Course completion requirements -
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)

The credit will be granted for

1. Attendance of all classes (maximum 3 absences).

2. Active work in the classes.

3. Successive solving of all the homework presented in the NMAI060 lecture as Exercises.

Literature -
Last update: doc. RNDr. Ivan Mizera, CSc. (05.10.2022)
  • Feller W., An Introduction to Probability Theory and its Applications, 3rd ed. J. Wiley, New York, 2008.
  • Prášková Z. a Lachout P. Základy náhodných procesů, Karolinum, Praha 1998.
  • Ross S.M. Introduction to Probability Models, 9th ed. Academic Press, Elsevier, London.
  • Lawler, G. F., Introduction to Stochastic Processes, Second Edition. Chapman and Hall/CRC, Boca Raton, 2006.

Teaching methods -
Last update: RNDr. Jitka Zichová, Dr. (14.05.2018)


Syllabus -
Last update: RNDr. Michal Kopecký, Ph.D. (12.05.2018)
  • 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.
  • Markov processes with discrete states and continuous time.
  • Models of birth and death.
  • Poisson process and its applications.
  • Basics of theory of queues, modeling of serving networks.
  • Exponential distribution and its use in the reliability theory.
  • Characteristics of reliability, survival times, intensity of failures and reliability of complex systems.

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