Course detail

# Mathematics 4

FAST-BA004Acad. year: 2022/2023

Discrete and continuous random variable and vector, probability function, density function, probability, cumulative distribution, transformation of random variables, independence of random variables, numeric characteristics of random variables and vectors, special distribution laws. Random sample, point estimation of an unknown distribution parameter and its properties, interval estimation of a distribution parameter, testing of statistical hypotheses, tests of distribution parameters, goodness-of-fit tests, basics of regression analysis.

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Course curriculum

2. Properties of probability. Cumulative distribution and its properties.

3. Relationships between probability, density and cumulative distributions. Marginal random vector.

4. Independent random variables. Numeric characteristics of random variables: mean and variance, standard deviation, variation coefficient, modus, quantiles. Rules of calculation mean and variance.

5. Numeric characteristics of random vectors: covariance, correlation coefficient, covariance and correlation matrices.

6. Some discrete distributions - discrete uniform, alternative, binomial, Poisson - definition, using.

7. Some continuous distributions - continuous uniform, exponential, normal, multivariate normal - definition applications.

8. Chi-square distribution, Student´s distribution - definition, using. Random sampling, sample statistics.

9. Distribution of sample statistics. Point estimation of distribution parameters, desirable properties of an estimator.

10. Confidence interval for distribution parameters.

11. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters.

12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.

13. Linear model.

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Prerequisites and corequisites

Basic literature

*Základy pravděpodobnosti.*CERM, 2011. 127 s. ISBN 978-80-7204-783-3. (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., DLOUHY, O.

*Sbírka příkladů z pravděpodobnosti a matematické statistiky.*CERM Brno, 2011. ISBN 978-80-7204-740-6. (CS)

KOUTKOVÁ, H. Elektronické studijní opory. M03 -

*Základy teroie odhadu,*M04 -

*Základy testování hypotéz*. FAST VUT Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp ] (CS)

Recommended reading

*Probability and Statistics for Engineers and Scientists*. 8th ed. London: Prentice Hall, Pearson education LTD, 2007.823 p. ISBN 0-13-204767-5. (EN)

Classification of course in study plans

- Programme B-P-C-MI (N) Bachelor's
branch MI , 2. year of study, winter semester, compulsory

- Programme B-P-E-SI (N) Bachelor's
branch S , 3. year of study, winter semester, compulsory

- Programme B-P-C-SI (N) Bachelor's
branch S , 3. year of study, winter semester, compulsory

- Programme B-K-C-SI (N) Bachelor's
branch S , 3. year of study, winter semester, compulsory

branch M , 3. year of study, winter semester, compulsory - Programme B-P-C-SI (N) Bachelor's
branch M , 3. year of study, winter semester, compulsory

- Programme B-P-E-SI (N) Bachelor's
branch M , 3. year of study, winter semester, compulsory

- Programme B-P-C-SI (N) Bachelor's
branch N , 3. year of study, winter semester, compulsory

branch K , 3. year of study, winter semester, compulsory - Programme B-K-C-SI (N) Bachelor's
branch K , 3. year of study, winter semester, compulsory

- Programme B-P-E-SI (N) Bachelor's
branch K , 3. year of study, winter semester, compulsory

branch V , 3. year of study, winter semester, compulsory - Programme B-P-C-SI (N) Bachelor's
branch V , 3. year of study, winter semester, compulsory

- Programme B-K-C-SI (N) Bachelor's
branch V , 3. year of study, winter semester, compulsory

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