639-0907/06 – Theory of Probability and Mathematical Statistics (TPMS)
| Gurantor department | Department of Quality Management | Credits | 10 |
| Subject guarantor | Ing. Filip Tošenovský, Ph.D. | Subject version guarantor | Ing. Filip Tošenovský, Ph.D. |
| Study level | postgraduate | Requirement | Choice-compulsory type B |
| Year | | Semester | winter + summer |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FMT, HGF | Intended for study types | Doctoral |
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:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Oral Exam
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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