Course detail

Probability and Mathematical Statistics

ÚSI-DSNA01Acad. year: 2025/2026

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

doc. RNDr. Jaromír Baštinec, CSc.

Department

Department of Mathematics (UMAT)

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BAŠTINEC, J., MPSO sbírka příkladů, Brbo 2016, 110 stran (CS)
BAŠTINEC, J., FAJMON, B., KOLÁČEK, J., Pravděpodobnost, statistika a operační výzkum. Brno 2014. 360 stran. (CS)

Recommended reading

BLITZSTEIN, Joseph K. a Jessica HWANG. Introduction to Probability. Boca Raton: CRC Press, 2019. ISBN 978-1138369917. (EN)
MATLOFF, Norman. Probability and Statistics for Data Science. Boca Raton: CRC Press, 2019. ISBN 978-0367331582. (EN)
RICE, John A. Mathematical Statistics and Data Analysis. Boston: Cengage Learning, 2020. ISBN 978-0357672937. (EN)
WASSERMAN, Larry. All of Statistics: A Concise Course in Statistical Inference. New York: Springer, 2018. ISBN 978-1441923226. (EN)

Classification of course in study plans

  • Programme DSP SoI_K Doctoral 1 year of study, summer semester, compulsory
  • Programme DSP SoI_P Doctoral 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Syllabus

  1. Pravděpodobnost, náhodná veličina, náhodný vektor.
  2. Rozdělení pravděpodobnosti pro aplikace.
  3. Průzkumová analýza pro zpracování statistických souborů.
  4. Náhodný výběr – model a vlastnosti.
  5. Fitování rozdělení pravděpodobnosti.
  6. Odhady parametrů rozdělení pravděpodobnosti.
  7. Testování statistických hypotéz o parametrech a rozděleních.
  8. Neparametrické testy.
  9. Základy lineární regresní analýzy.
  10. Úvod do analýzy rozptylu.
  11. Úvod do kategoriální analýzy.
  12. Statistický software – vlastnosti a možnosti použití.
  13. Aplikace statistických metod na reálných příkladech

Guided consultation in combined form of studies

6 hod., optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Guided consultation

9 hod., optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.