Course Details

# Probability and mathematical statistics

DAB039 course is part of 4 study plans

Ph.D. full-t. program DPC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-GK compulsory-elective Summer Semester 1st year 4 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.

Course Guarantor

Ing. Jan Holešovský, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

Probability and statistics are used in numerous fields of civil engineering. The course aims to teach the students how to deal with practical probability problems using the basic statistical methods, particularly interval estimation of parametric functions, testing both parametric and nonparametric statistical hypotheses.

Prerequisites

Basics of linear algebra, differentiation, integration.

Corequisites

Not required.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The final examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

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

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

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.