Course detail

Probability and Mathematical Statistics

ÚSI-DSA02Acad. year: 2024/2025

The course is intended for doctoral students and is focused on stochastic modelling and modern methods of statistical analysis (probability, random variables and vectors, random selection and its realization, fitting of probability distributions and estimates of their parameters, testing, of statistical hypotheses, regression analysis) for processing statistical files obtained in the implementation and evaluation of experiments in the framework of students' research work.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

RNDr. Helena Koutková, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Introduction to probability calculus and descriptive statistics to the extent of the master's degree program.

Rules for evaluation and completion of the course

The exam is in the form of a presented paper from a selected area of statistical methods or a written work aimed at solving specific tasks.

Aims

The aim of the course is to form the stochastic way of thinking of students and their introduction to modern stochastic methods and inductive methods of mathematical statistics, including the possibilities and application of professional statistical software in research.

Students will acquire deeper knowledge of stochastic modelling and modern methods of mathematical statistics, which will enable them to apply adequate stochastic models of observed phenomena and processes by means of PC calculations.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ANDĚL, J.: Statistické metody, MATFYZPRESS Praha, 1993
DOWDY, S., WEARDEN, S., CHILKO, D. Statistics for Research. New York: John Wiley & Sons, Inc., 2011. (CS)
KOUTKOVÁ,H., MOLL,I.: Úvod do pravděpodobnosti a matematické statistiky, CERM Brno, 2001
MONTGOMERY, D. C., RUNGER, G. Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, Inc., 2011. (CS)

Recommended reading

HEBÁK, P., HUSTOPECKÝ, J., JAROŠOVÁ, E., PECÁKOVÁ, I. Vícerozměrné statistické metody (1), (2), (3), Praha: Informatorium, 2004. (CS)
KARPÍŠEK, Z. Matematika IV. Pravděpodobnost a matematická statistika. Brno: CERM, 2014. (CS)
KOŽÍŠEK, J., STIEBEROVÁ, B. Statistika v příkladech. Praktické aplikace řešené v MS Excel. Praha: Verlag Dashofer, 2012. (CS)
WALPOLE, R.E., MYERS, R.H.: Probability and Statistics for Engineers and Scientists, MACMILLIAN PUBLISHING COMPANY, New York, 1999

Classification of course in study plans

  • Programme DSoIK Doctoral

    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory

  • Programme DSoIP Doctoral

    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory
    branch SOI , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

39 hod., compulsory

Teacher / Lecturer

RNDr. Helena Koutková, CSc.

Syllabus

1. Probability, random variable, random vector.
2. Probability distribution for applications.
3. Exploratory analysis for processing statistical files.
4. Random selection - model and properties.
5. Fitting the probability distribution.
6. Estimation of probability distribution parameters.
7. Testing statistical hypotheses about parameters and distributions.
8. Nonparametric tests.
9. Basics of linear regression analysis.
10. Introduction to analysis of variance.
11. Introduction to categorical analysis.
12. Statistical software - features and applications.