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ECTS Course Overview

Mathematical Statistics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code639-2002/05
Number of ECTS Credits Allocated7 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *First Cycle
Year of Study *
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English, Spanish
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
TOS40prof. RNDr. Josef Tošenovský, CSc.
TOS012Ing. Filip Tošenovský, Ph.D.
The subject Mathematical Statistics follows up on probability theory. It uses tools of probability to present estimation of population parameters, hypothesis testing, modelling of technological processes with regression models and their assessment by correlation analysis. Multivariate regression is taught under the necessary theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables.
Learning Outcomes of the Course Unit
Knowlege of Basic statistical Methods
Analysis of Experimental Data
Course Contents
1. Population and sample, random sample, frequencies
2. Division of data into classes (procedure and reason for doing so), histogram
3. Moment and quantile characteristics
4. The theorem on a single drawing from normal distribution and its use
5. The theorem on two drawings from normal distribution and its use
6. Hypothesis testing – general procedure, type I and II errors in testing
7. F-test, t-tests (all steps taken in the test)
8. Correlation analysis (the r coefficient and its testing, correlation index, condition for use, properties)
9. Multivariate regression analysis (principal matrix formulae)
10. Spearmann’s correlation coefficient, contingency tables
11. Point estimation of
12. Interval estimation of
13. Test of normality (skewness and kurtosis of normal distribution, Shapiro-Wilk test and its table of critical values)
14. Testing of outliers (Grubb’s test, Box Plot), tests of data independence (sign test).
Recommended or Required Reading
Required Reading:
JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7.

ANDĚL, J. Základy matematické statistiky. Praha: MATFYZPRESS, 2011. ISBN 978-80-737-8162-0.
TOŠENOVSKÝ, J. Základy statistického zpracování dat. Ostrava: VŠB - Technická univerzita Ostrava, 2015. ISBN 978-80-248-3733-8.
JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introductuion to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7.

Recommended Reading:
MONTGOMERY, D. C. Applied Statistics and Probability for Engineers. NY: Wiley, 2010. ISBN-13 978-1-1185-3971-2.
SHESKIN, D. J. Handbook of Parametric and Nonparametric Statistical Procedures. NY: Chapman and Hall, 2003. ISBN 1-58488-440-1.
MELOUN, J. a J. MILITKÝ. Statistické zpracování experimentálních dat. Praha: Ars magna, 1998. ISBN 80-7219-003-2.
HANOUSEK, J. a P. CHARAMZA. Moderní metody zpracování dat. Matematická
statistika pro každého. Praha: EDUCA, 1992. ISBN 80-85623-31-5.
TOŠENOVSKÝ, J. a D. NOSKIEVIČOVÁ. Statistické metody pro zlepšování jakosti.
Ostrava: Montanex, 2000. ISBN 80-7225-040-X.
LIKEŠ, J. a J. MACHEK. Matematická statistika. Praha: SNTL, 1983.

Planned learning activities and teaching methods
Lectures, Seminars, Tutorials, Project work
Assesment methods and criteria
Tasks are not Defined