639-0907/07 – Theory of Probability and Mathematical Statistics (TPMS)

Gurantor departmentDepartment of Quality ManagementCredits10
Subject guarantorprof. RNDr. Josef Tošenovský, CSc.Subject version guarantorprof. RNDr. Josef Tošenovský, CSc.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMT, HGFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
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 Examination 20+0
Part-time Examination 20+0

Subject aims expressed by acquired skills and competences

Students will demonstrate knowledge of selected methods of the theory of probability and mathematical statistics. They will be able to carry out analyses of real-life data and justify theoretically all necessary operations.

Teaching methods

Individual consultations
Project work

Summary

The subject follows up on probability theory. It uses the 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 required theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables.

Compulsory literature:

JAMES, G., D. WITTEN, T. HASTIE and R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7. KUTNER, M. H.,CH. J. NACHTSHEIM and J. NETER. Applied Linear Regression Models. NY:McGraw-Hill, 2004. ISBN 0-07-301344-7. BOX,G. E. P.,HUNTER,W.G. and J.S. HUNTER. Statistics for Experimenters. NY: Wiley&Sons, 1978. ISBN 0-471-09315-7.

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

E-learning

Other requirements

1) Knowledge of elementary terms of the probability theory: random variable, random vector, random variable function

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Definition of terms: experiment, event, probability of an event, random variable. 2. Axiomatic, classical and statistical definition of probability. 3. Theorems on probability calculus. 4. Probability density and probability distribution functions: definition, properties. 5. Distributions: normal, binomial, Poisson, Pearson’s, Fischer’s. 6. Function of a random variable. 7. Characteristics of a random vector. Multinomial and multivariate normal distribution. 8. Population and sample. Generation of random numbers. 9. Quantile characteristics. 10. Theorems on one sample and two samples from a normal distribution. 11. Confidence intervals: derivation, basic formulas. 12. Testing of Hypothesis: general procedure, errors in testing. 13. Tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk, sign test of independence, Kruscal-Wallis, Wilcoxon. 14. Simple linear regression, model analysis. Assumptions of linear regression and their verification. 15. Multiple linear and nonlinear regression. 16. Analysis of variance (ANOVA). 17. Analysis of correlation. 18. Contingency tables, qualitative variables in regression analysis.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (P0413D270001) Management of Industrial Systems P English Ostrava Choice-compulsory type B study plan
2020/2021 (P0413D270001) Management of Industrial Systems K English Ostrava Choice-compulsory type B study plan
2019/2020 (P0413D270001) Management of Industrial Systems P English Ostrava Choice-compulsory type B study plan
2019/2020 (P0413D270001) Management of Industrial Systems K English Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner