Czech

5

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Institute of Mathematics and Descriptive Geometry (MAT)

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

The students should be familiar with the subjects taught in the Mathematics I and Mathematics II courses.

Not applicable.

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Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

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.
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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: 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)

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, obligation not entered