Course detail

Probability and Statistics II

FSI-SP2Acad. year: 2025/2026

This course is concerned with the following topics: multidimensional normal distribution, linear regression model (estimates, tests of hypotheses, regression diagnostics), nonlinear regression model, introduction to ANOVA, correlation analysis, basic methods of categorical analysis. Students learn about the applicability of those methods and available software for computations.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. Mgr. Zuzana Hübnerová, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Rudiments of descriptive statistics, probability theory and mathematical statistics.

Rules for evaluation and completion of the course

Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing all written exams, and semester assignment acceptance. Preparing and defending a project.

Examination: written form of the exam (70 points) and oral part (30 points): a practical written part (4 tasks related to random vectors, conditional distribution, multivariate normal distribution, regression analysis, correlation analysis, categorical data analysis); theoretical oral part (4 tasks related to basic notions, their properties, sense and practical use, and proofs of two theorems); evaluation according to the total number of points (scoring 0 points for any of 4 practical tasks or whole theoretical part means failing the exam): excellent (90 - 100 points and both proofs), very good (80 - 89 points and both proofs), good (70 - 79 points and one proof), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).


Participation in the exercise is mandatory and the teacher decides on the compensation for absences.

Aims

The course objective is to make students majoring in Mathematical Engineering acquainted with theoretical background of regression analysis and with real applications of regression methods in technical practice.

Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and apply them on PC.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anděl, J.: Matematická statistika. Praha : SNTL, 1978. (CS)
Anděl, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005. (CS)
Lamoš, F. - Potocký, R.: Pravdepodobnosť a matematická štatistika. Bratislava : Alfa, 1989.
Montgomery, D. C. - Runger, G.: Applied Statistics and Probability for Engineers, John Wiley & Sons, New York. 2002. (EN)

Recommended reading

Anděl, J.: Statistické metody. Praha : Matfyzpress, 2007. (CS)
Hebák, P. et al.: Vícerozměrné statistické metody (1), (2). Praha : Informatorium, 2004, 2005. (CS)
Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2014. (CS)
Zvára, K.: Regrese. Praha: Matfyzpress. 2008. (CS)

Classification of course in study plans

  • Programme B-MAI-P Bachelor's 3 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

Random vector, moment characteristics.
Conditional distribution.
Characteristic function.
Multivariate normal distribution - properties.
Distribution of quadratic forms.
Linear regression model (LRM) and parameter estimates in LRM.
Testing hypotheses concerning linear regression model.
Special cases of LRM (regression line, regression parabola, polynomial regression, ANOVA models).
Weighted regression, an introduction to regression diagnostic and linearized regression model.
Correlation analysis
Goodness of fit tests with known and unknown parameters
Introduction to categorical data analysis (chi-square test, measures of association, Fisher factorial test).

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

Random vector, variance-covariance matrix, correlation matrix.
Conditional distribution, conditional expectation, conditional variance.
Characteristic function - examples, properties.
Properties of the multivariate normal distribution, linear transformation.
Distributions of quadratic forms - examples for normal distribution.
Point and interval estimates of coefficients, variance and values of linear regression function. Statistical software on PC
Testing hypotheses concerning linear regression functions: particular and simultaneous tests of coefficients, tests of model.
Multidimensional linear and nonlinear regression functions and diagnostics on PC.
Correlation coefficients, partial and multiple correlations.
Goodness of fit tests on PC.
Analysis of categorical data: contingency table, chi-square test, Fisher test.