Course detail

Probability and Mathematical Statistics

ÚSI-DSNA01Acad. year: 2021/2022

The course is intended for doctoral students and is focused on stochastic modelling and modern methods of statistical analysis (probability, random variables and vectors, random selection and its realization, fitting of probability distributions and estimates of their parameters, testing, of statistical hypotheses, regression analysis) for processing statistical files obtained in the implementation and evaluation of experiments in the framework of students' research work.

Learning outcomes of the course unit

Not applicable.


Introduction to probability calculus and descriptive statistics to the extent of the master's degree program.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

BAŠTINEC, J., FAJMON, B., KOLÁČEK, J., Pravděpodobnost, statistika a operační výzkum. Brno 2014. 360 stran. (CS)
BAŠTINEC, J., MPSO sbírka příkladů, Brbo 2016, 110 stran (CS)
Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for engineers. 6th Edition. John Wiley \& Sons, Inc., New York 2015.ISBN-13: 978-1118539712. (EN)
LOFTUS, J., LOFTUS, E., Essence of Statistics. Second Edition. Alfred A.Knopf, New York 1988. (EN)
TAHA, H.A., Operations research. An introduction. Fourth Edition. Macmilan Publishing Company, New York 1989. (EN)
DEVORE, J.L., Probability ans Statistics for Engineering and the Sciences, 8th edition, ISE, ISBN 978-0-8400-6827-9 (EN)
FREUND, J.E., WILSON, W.J., MOHR, D. L., Statistical methods, 3rd edition, Elsevier, 2010, ISBN 978-0-12-374970-3 (EN)

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

The exam is in the form of a presented paper from a selected area of statistical methods or a written work aimed at solving specific tasks.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Probability, random variable, random vector.
2. Probability distribution for applications.
3. Exploratory analysis for processing statistical files.
4. Random selection - model and properties.
5. Fitting the probability distribution.
6. Estimation of probability distribution parameters.
7. Testing statistical hypotheses about parameters and distributions.
8. Nonparametric tests.
9. Basics of linear regression analysis.
10. Introduction to analysis of variance.
11. Introduction to categorical analysis.
12. Statistical software - features and applications.


The aim of the course is to form the stochastic way of thinking of students and their introduction to modern stochastic methods and inductive methods of mathematical statistics, including the possibilities and application of professional statistical software in research.

Classification of course in study plans

  • Programme DSP SoI_P Doctoral, 1. year of study, summer semester, 0 credits, compulsory
  • Programme DSP SoI_K Doctoral, 1. year of study, summer semester, 0 credits, compulsory

Type of course unit



24 hours, optionally

Teacher / Lecturer

Guided consultation in combined form of studies

6 hours, optionally

Teacher / Lecturer

Guided consultation

8 hours, optionally

Teacher / Lecturer