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, 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. 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.

Not applicable.

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)