Gurantor department | Department of Quality Management | Credits | 10 |

Subject guarantor | prof. RNDr. Josef Tošenovský, CSc. | Subject version guarantor | prof. RNDr. Josef Tošenovský, CSc. |

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 |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

TOS012 | Ing. Filip Tošenovský, Ph.D. | ||

TOS40 | prof. RNDr. Josef Tošenovský, CSc. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Examination | 20+0 |

Part-time | Examination | 20+0 |

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.

Individual consultations

Project work

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.

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.

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.

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

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
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Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2021/2022 | (P0413D270002) Management of Industrial Systems | K | Czech | Ostrava | Choice-compulsory type B | study plan | ||||||

2021/2022 | (P0413D270002) Management of Industrial Systems | P | Czech | Ostrava | Choice-compulsory type B | study plan | ||||||

2020/2021 | (P0413D270002) Management of Industrial Systems | K | Czech | Ostrava | Choice-compulsory type B | study plan | ||||||

2020/2021 | (P0413D270002) Management of Industrial Systems | P | Czech | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0413D270002) Management of Industrial Systems | P | Czech | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0413D270002) Management of Industrial Systems | K | Czech | Ostrava | Choice-compulsory type B | study plan |

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