Czech

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Student will be able to solve simple practical probability problems and to use basic statistical methods for interval estimates, testing parametric and non-parametric statistical hypotheses, and linear models.

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.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

A student will only receive credit if he or she has attended all the workshops and passes a written test with at least 50-percent success.
An exam with a pass rate of at least 50% will follow. The examination will be only a written one lasting 90 minutes and consisting of 3 practical problems to calculate and one problem with questions about the theoretical background.

1. Continuous and discrete random variable (vector), probability function, density function. Probabilty.
2. Properties of probabilty. Cumulative distribution and its properties.
3. Relationships between probabilty, density and cumulative distributions. Marginal distribution.
4. Independent random variables. Charakteristics of random variables : mean and variance,percentiles. Rules of calculation mean and variance.
5.Charakteristics of random variables: covariance, correlation coefficient. Correlation matrices.
6.Some discrete distributions - discrete uniform, alternative, binomial, Poisson - definitoin, using.
7. Some continuous distributions - continuous uniform, exponential, normal.
8. Chi-squared distribution, Student´s distribution - definition, using . Random sampling, statistic.
9. Point estimate of distribution parameter, desirable properties of an estimator.
10. Confidence interval for distribution parameter.
11. Fundamentals for testing hypotheses. Tests of hypotheses for normal distribution parameters.
12. Goodness-of-fit test. Basics of regression analysis.
13. Linear model.
___________________________________
Practice:
1. Empirical probability and density distributions. Histogram.
2. Probability and density distributions. Probability.
3. Cumulative distribution. Relationships between probabilty, density and cumulative distributions.
5. Function of random variable.
6. Calculation of mean, variance and percentiles of random variable. Calculation rules of mean and variance.
7. Correlation coefficient.
8. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson.
9. Calculation of probability in case of normal distribution. Work with statistical tables.
10. Calculkation of sample statistcs.
11.Confidence interval for normal distribution parametres.
12. Tests of hypotheses for normal distribution parametres.
13. Goodness-of-fit test.

Not applicable.

The students should get an overview of teh 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.

Not applicable.

Not applicable.

KOUTKOVÁ, Helena, DLOUHY, Oldřich: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno, 2011. ISBN 978-80-7204-740-6. (CS)
KOUTKOVÁ, Helena, MOLL, Ivo: Základy pravděpodobnosti. CERM, 2011. ISBN 978-80-7204-783-3. (CS)
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)

ANDĚL, Jiří: Statistické metody. MATFYZPRESS, Praha, 2007. ISBN 8-07-378003-8. (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)