Czech

3

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 from the fields of interval estimates,and testing parametric and non-parametric statistical hypotheses.

Basics of the theory of one- and more-functions (derivative, partial derivative, limit and continuos functions, graphs of functions). Calculation of indefinite integrals, knowledge of their basic applications.

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. Probability.
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 variable: mean and variance,percentiles. Rules of calculation mean and variance.
5. Charakteristics of random vectors: covariance, correlation coefficient. Normal distribution - definition, using.
6. Chi-squared distribution, Student´s distribution. Random sampling, statistic.
7. Point estimate of distribution parameter, desirable properties of an estimator.
8. Confidence interval for distribution parameter.
9. Fundamentals for testing hypotheses. Tests of hypotheses for normal distribution parameters.
10. Goodness-of-fit test.
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Practice:
1. Empirical probability and density distributions. Histigram. Probability and density distributions.
2. Probability. Cumulative distribution.
3. Relationships between probabilty, density and cumulative distributions.
4. Function of random variable.
5. Calculation of mean, variance and percentiles of random variable. Calculation rules of mean and variance.
6. Correlation coefficient. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson.
7. Calculation of probability in case of normal distribution. Work with statistical tables. Calculation of point estimators.
8. Confidence interval for normal distribution parametres.
9. Tests of hypotheses for normal distribution parametres.
10. Goodness-of-fit test.

Not applicable.

After the course, the students should undertand the basics of the theory of probability, work with distribution functions, know the meanig and methods of calculation of basic numeric characteristics of random variables and vectors, know how a normal random variable is defined and what is its principal meaning, know how to calculate the probability in special cases of discrete and continuous diostribution laws, know how to determine the distribution of a transformed random variable.
They should be able to interpret the basic concepts of the mathematical statistics - sampling, point estimates of distribution parameters and the reqiured properties of an estimate. They should know what an interval estimate of a distribution parameter is and be able to calculate such inerval estimates of the parameters of a normal random variable. They should know the basics of the testing of statistical hypotheses, know how to test hypotheses on the parameters of a normal random variable and on the shape of a distribution law.

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

Not applicable.

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KOUTKOVÁ, H.  M03 Základy teorie odhadu a M04 Základy testování hypotéz. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)
KOUTKOVÁ, H. Základy teorie odhadu .Brno: CERM, 2007,  51 s. ISBN 978-80-7204-527-3.   (CS)
KOUTKOVÁ, H. Základy testování hypotéz. Brno: CERM, 2007, 52 s. ISBN 978-80-7204-528-0. (CS)

WALPOLE, R.E., MYERS, R.H. Probability and Statistics for Engineers and Scientists. New York: Macmillan Publishing Company, 1990, 823 p. ISBN 0-02-946910-4. (EN)
ANDĚL, J. Statistické metody. Praha: MatFyzPress, 2007, 299 s. ISBN 80-7378-003-8.  (CS)

26 hours, obligation not entered