Course detail

Probability and mathematical statistics

FAST-DA62OptionalDoctoral (3rd cycle)Acad. year: 2017/2018Summer semester1. year of study4  credits

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.

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

ANDĚL, J.: Statistické metody. MATFYZPRESS PRAHA 2007
KOUTKOVÁ, H., MOLL, I.: Základy pravděpodobnosti. CERM Brno 2011
KOUTKOVÁ, H.: Základy teorie odhadu. CERM Brno 2007
KOUTKOVÁ, H.: Základy testování hypotéz. CERM Brno 2007
KOUTKOVÁ, H., DLOUHÝ, O.: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno 2011
WALPOLE, R.E., MYERS, R.H.: Probability and Statistics for Engineers and Scientists. Macmillan Publishing Company New York 1990

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

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.

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.

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer