Course Details

Probability and mathematical statistics

Academic Year 2023/24

DA62 course is part of 11 study plans

​ D-P-C-SI (N) / PST Summer Semester 1st year

​ D-P-C-SI (N) / FMI Summer Semester 1st year

​ D-P-C-SI (N) / KDS Summer Semester 1st year

​ D-P-C-SI (N) / MGS Summer Semester 1st year

​ D-P-C-SI (N) / VHS Summer Semester 1st year

​ D-K-C-SI (N) / VHS Summer Semester 1st year

​ D-K-C-SI (N) / MGS Summer Semester 1st year

​ D-K-C-SI (N) / PST Summer Semester 1st year

​ D-K-C-SI (N) / FMI Summer Semester 1st year

​ D-K-C-SI (N) / KDS Summer Semester 1st year

​ D-K-E-SI (N) / PST Summer Semester 1st year

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.

Credits

4 credits

Language of instruction

Czech

Semester

summer

Course Guarantor

RNDr. Helena Koutková, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit

Entry Knowledge

Basics of linear algebra, differentiation, integration.

Aims

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

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)

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.

Prerequisites

Basics of linear algebra, differentiation, integration.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

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

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/272116

Lecture

13 weeks, 3 hours/week, elective

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.