639-2002/03 – Mathematical Statistics (MS)

Gurantor departmentDepartment of Quality ManagementCredits5
Subject guarantorprof. RNDr. Josef Tošenovský, CSc.Subject version guarantorprof. RNDr. Josef Tošenovský, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2015/2016Year of cancellation2020/2021
Intended for the facultiesFMTIntended for study typesBachelor, Follow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAL37 Ing. Mgr. Petra Halfarová, Ph.D.
TOS012 Ing. Filip Tošenovský, Ph.D.
TOS40 prof. RNDr. Josef Tošenovský, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 18+0

Subject aims expressed by acquired skills and competences

Knowlege of Basic statistical Methods Analysis of Experimental Data

Teaching methods

Project work


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.

Compulsory literature:

JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7.

Recommended literature:

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.

Way of continuous check of knowledge in the course of semester

Test Essay


E-learning: Integrovaný systém modulární počítačové výuky ekonomicko-technického zaměření (http://lms.vsb.cz): Vzdělávací modul 4 – Zlepšování procesů s využitím statistické analýzy, submodul Průzkumová analýza dat: Grafické nástroje (s. 3 – 21) Intervalové odhady (s. 25 – 33) Testování hypotéz (s. 33 – 67) Regresní analýza (s. 73 – 90) TOŠENOVSKÝ, J. Plánování experimentů. Studijní opory. Ostrava: VŠB-TU Ostrava, 2012. TOŠENOVSKÝ, J. Teorie pravděpodobnosti. Studijní opory. Ostrava: VŠB-TU Ostrava, 2012.

Other requirements

Submission of projects, the successful completion of tests during the semester, active participation in the lesson. Development of two specified programs, each in the range of 4 s theme of the program.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

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).

Conditions for subject completion

Full-time form (validity from: 2017/2018 Summer semester, validity until: 2020/2021 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40  20
        Examination Examination 60  31
Mandatory attendence parzicipation: 80%

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N3923) Materials Engineering (3911T033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2018/2019 (N3923) Materials Engineering (3911T033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3923) Materials Engineering (3911T033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3923) Materials Engineering (3911T033) Material Recycling P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner