Course detail

Probability and mathematical statistics

FAST-DA62Acad. year: 2023/2024

Continuous and discrete random variables (vectors), probability function, density function, probability, cumulative distribution, independent random variables, characteristics of distribution, transformation of random variables, conditional distribution, conditional mean, special distributions.
Random sampling, statistic, point estimate of distribution parameters and their functions, desirable properties of an estimator, estimator of correlation matrix, confidence interval for distribution parameter, fundamentals for testing hypotheses, tests of hypotheses for distribution parameters - one-sample analysis, two-sample analysis, goodness-of-fit test.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Helena Koutková, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Basics of linear algebra, differentiation, integration.

Rules for evaluation and completion of the course

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

Aims

The correct grasp of the basic concepts and art of interpreting statistical outcomes.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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. 8th ed. London: Prentice Hall, Pearson education LTD, 2007. 823 p. ISBN 0-13-204767-5.   (EN)
HRON, A., KUNDEROVÁ, P. Základy počtu pravděpodobnosti a metod matematické statistiky. 2. vyd. Olomouc: UPOL, 2015. 364 s. ISBN 978-80-244-4774-2.  (CS)

Recommended reading

KOUTKOVÁ, H., MOLL, I. Základy pravděpodobnosti. Brno: CERM, 2011.127 s. ISBN 978-80-7204-738-3. (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)

Classification of course in study plans

  • Programme D-P-C-SI (N) Doctoral

    branch PST , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-E-SI (N) Doctoral

    branch PST , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch PST , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-E-SI (N) Doctoral

    branch MGS , 1. year of study, summer semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch KDS , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch KDS , 1. year of study, summer semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch MGS , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch MGS , 1. year of study, summer semester, compulsory-optional
    branch FMI , 1. year of study, summer semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch FMI , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-E-SI (N) Doctoral

    branch FMI , 1. year of study, summer semester, compulsory-optional
    branch KDS , 1. year of study, summer semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch VHS , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-E-SI (N) Doctoral

    branch VHS , 1. year of study, summer semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch VHS , 1. year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

RNDr. Helena Koutková, CSc.

Syllabus

1. - 8. Continuous and discrete random variables (vectors), probability function, density function, probability, cumulative distribution, independent random variables, characteristics of distribution, transformation of random variables, conditional distribution, conditional mean, special distributions. 9. - 13. Random sampling, statistic, point estimate of distribution parameters and their functions, desirable properties of an estimator, estimator of correlation matrix, confidence interval for distribution parameter, fundamentals for testing hypotheses, tests of hypotheses for distribution parameters - one-sample analysis, two-sample analysis, goodness-of-fit test.