Czech

5

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Not applicable.

Basics of the theory of one- and more-functions (derivative, partial derivative, limit and continuous functions, graphs of functions). Calculation of definite integrals, double and triple integrals, knowledge of their basic applications.

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1. Continuous and discrete random variable (vector), probability function, density function. Probability.
2. Properties of probability. Cumulative distribution and its properties.
3. Relationships between probability, density and cumulative distributions. Marginal random vector and its distribution.
4. Independent random variables. Numeric characteristics of random variables: mean and variance, standard deviation, variation coefficient, modus, quantiles. Rules for calculating mean and variance.
5. Numeric characteristics of random vectors: covariance, correlation coefficient, covariance and correlation matrices.
6. Some discrete distributions - discrete uniform, alternative, binomial, Poisson - definition, applications.
7. Some continuous distributions - uniform, exponential, normal, multivariate normal - definition applications.
8. Chi-square distribution, Student´s distribution - definition, applications. Random sampling, sample statistics.
9. Distribution of sample statistics. Point estimation of distribution parameters, desirable properties of an estimator - definition, interpretation.
10. Confidence interval for distribution parameters.
11. Fundamentals for testing hypotheses. Tests of hypotheses for normal distribution parameters.
12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
13. Linear model.

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The students should get an overview of the basic properties of probability to be able to deal with simple practical problems in probability. They should get familiar with the basic statistical methods used for interval estimates, testing statistical hypotheses, and linear model.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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KOUTKOVÁ, Helena: M03 Základy teorie odhadu a M04 Základy testování hypotéz. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)
KOUTKOVÁ, Helena: Základy teorie odhadu. CERM, Brno, 2007. ISBN 978-80-7204-527-3. (CS)
KOUTKOVÁ, Helena: Základy testování hypotéz. CERM, Brno, 2007. ISBN 978-80-7204-528-0. (CS)
KOUTKOVÁ, Helena, MOLL, Ivo: Základy pravděpodobnosti. CERM Brno, 2011. ISBN 978-80-7204-738-3. (CS)
KOUTKOVÁ, Helena, DLOUHY, Oldřich: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno, 2011. ISBN 978-80-7204-740-6. (CS)

WALPOLE, R.E., MYERS, R.H.: Probability and Statistics for Engineers and Scientists. Macmillan Publishing Company, New York, 1990. ISBN 0-02-946910-4. (EN)
ANDĚL, Jiří: Statistické metody. MATFYZPRESS, Praha, 2007. ISBN 8-07-378003-8. (CS)

26 hours, compulsory