M6444 Stochastic models of Markov type

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
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