M6444 Stochastic models of Markov type

Faculty of Science
Spring 2017
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (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
Timetable
Mon 20. 2. to Mon 22. 5. Mon 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M6444/01: Mon 20. 2. to Mon 22. 5. Tue 9:00–9:50 MP1,01014, Tue 9:00–9:50 M3,01023, M. Budíková
M6444/02: Mon 20. 2. to Mon 22. 5. Tue 10:00–10:50 MP1,01014, Tue 10:00–10:50 M3,01023, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
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 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 1 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
Study Materials
The course is taught annually.
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 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2017, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2017/M6444