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Theory of Probability and Mathematical Statistics

Type of study Doctoral
Language of instruction Czech
Code 639-0907/02
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

• Definition of terms: experiment, event, probability of an event,
random variable.
• Axiomatic, classical and statistical definition of probability.
• Theorems on probability calculus.
• Probability density and probability distribution functions:
definition, properties.
• Distributions: normal, binomial, Poisson, Pearson’s, Fischer’s.
• Function of a random variable.
• Characteristics of a random vector. Multinomial and multivariate
normal distribution.
• Population and sample. Generation of random numbers.
• Quantile characteristics.
• Theorems on one sample and two samples from a normal distribution.
• Confidence intervals: derivation, basic formulas.
• Testing of Hypothesis: general procedure, errors in testing.
• Tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk, sign test of
independence, Kruscal-Wallis, Wilcoxon.
• Simple linear regression, model analysis.
• Assumptions of linear regression and their verification.
• Multiple linear and nonlinear regression.
• Analysis of variance (ANOVA).
• Analysis of correlation.
• 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 .