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Theory of Probability and Mathematical Statistics

Type of study Doctoral
Language of instruction Czech
Code 639-0907/06
Abbreviation TPMS
Course title Theory of Probability and Mathematical Statistics
Credits 10
Coordinating department Department of Quality Management
Course coordinator Ing. Filip Tošenovský, Ph.D.

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.

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 .

Advised 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 .