Course Details

Probability and mathematical statistics

DA62 course is part of 20 study plans

Ph.D. full-t. program nD > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > KDS 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

RNDr. Helena Koutková, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Prerequisites

Basics of linear algebra, differentiation, integration.

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.

Objective

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

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.