Course detail

# Probability and mathematical statistics

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. Ongoing information on the possibility of using statistical software in the application of the subject matter discussed.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Basics of linear algebra, differentiation, integration.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

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.

Work placements

Not applicable.

Aims

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

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

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.  (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)

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 DKC-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-V Doctoral, 1. year of study, summer semester, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

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.