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 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 continuous functions, graphs of functions). Calculation of definite integrals, knowledge of their basic applications.

Not applicable.

Not applicable.

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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 of random variable. Marginal random vector and its distribution.
4. Independent random variables. Numeric characteristics of random variable: mean and variance, quantiles. Rules of calculation mean and variance.
5. Numeric characteristics of random vectors: covariance, correlation coefficient. Normal distribution - definition, using.
6. Chi-square distribution, Student´s distribution. Random sampling, sample statistics.
7. Point estimation of distribution parameters, desirable properties of an estimator - definition, interpretation.
8. Confidence interval for distribution parameters.
9. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters.
10. Goodness-of-fit tests.

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., DLOUHÝ, O. Sbírka příkladů z pravděpodobnosti a matematické statistiky. Brno: CERM,2011, 63 s. ISBN 978-80-7204-740-6. (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)
KOUTKOVÁ, H., MOLL, I. Základy pravděpodobnosti. Brno: CERM, 2011, 127 s. ISBN 978-80-7204-738-3. (CS)
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)

ANDĚL, J. Statistické metody. Praha: MatFyzPress, 2007, 299 s. ISBN 80-7378-003-8.  (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)