Course detail

Probability and mathematical statistics

FAST-DAB039Acad. 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

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jiří Novotný, 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

Not applicable.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ANDĚl, J. Statistické metody. 3. vyd. Praha: MatFyzPress, 2019, 300 s. ISBN: 978-80-7378-381-5.
HRON, A., KUNDEROVÁ, P. Základy počtu pravděpodobnosti a metod matematické statistiky. 2. vyd. Olomouc: UPOL, 2015, 364 s. ISBN 978-80-244-4774-2.
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.

Recommended reading

KOUTKOVÁ, H., MOLL, I. Základy pravděpodobnosti. Brno: CERM, 2011, 127 s. ISBN 978-80-7204-738-3.
KOUTKOVÁ, H. Základy teorie odhadu. Brno: CERM, 2007, 51 s. ISBN 978-80-7204-527-3.
KOUTKOVÁ, H. Základy testování hypotéz. Brno: CERM, 2007, 52 s. ISBN 978-80-7204-528-0.

Classification of course in study plans

  • Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
  • Programme DPA-GK Doctoral 1 year of study, summer semester, compulsory-optional
  • Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
  • Programme DKA-GK Doctoral 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

Ing. Jan Holešovský, Ph.D.

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.