Course detail

Mathematical Statistics

FP-mstPAcad. year: 2026/2027

Understanding the basic principles of mathematical statistics. Ability to process and analyze data sets. Application of statistical methods for estimation and hypothesis testing. Modeling and analyzing data using regression models and time series.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

Ing. Karel Doubravský, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Not applicable.

Rules for evaluation and completion of the course

COMPLETION OF THE COURSE

Credit is awarded on the basis of:
- completion of the semester assignments (the topic of the assignments will be specified during the semester);
- active participation in the exercises.

The exam is written with the use of computer technology and consists of:
- solving four examples;
- answering a theoretical question;
- 120 minutes to complete the exam.

A mark, corresponding to a total (max. 100 points), consisting of:
- the score of the semester assignments (max. 40 points);
- the results of the solved examples (max. 48 points);
- the quality of the answers to the theoretical question (max. 12 points).

Grades and their corresponding points:
A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), F (49-0).

Attendance at lectures is not compulsory but is recommended. Attendance at tutorials is supervised.
Any non-participation greater than 20 % will be made up with make-up assignments.

COMPLETION OF THE COURSE FOR STUDENTS WITH INDIVIDUAL STUDIES

Credit is awarded based on:
- completion of semester assignments.

The examination is written using computer technology and consists of:
- solving four examples;
- answering a theoretical question;
- given 120 minutes to complete the examination.

A mark, corresponding to a total (max. 100 points), consisting of:
- the score of the semester assignments (max. 40 points);
- the results of the solved examples (max. 48 points);
- the quality of the answers to the theoretical question (max. 12 points).

Grades and corresponding points:
A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), F (49-0).

Aims

Understanding the basic principles of mathematical statistics. Ability to process and analyze data sets. Application of statistical methods for estimation and hypothesis testing. Modeling and analyzing data using regression models and time series.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DEVORE, Jay L.; BERK, Kenneth N a CARLTON, Matthew A. Modern mathematical statistics with applications. 3. vydání. Cham: Springer, 2021. ISBN 978-3-030-55158-2. (EN)
KROPÁČ, Jiří. STATISTIKA B. 3. vydání Brno: Akademické nakladatelství CERM, 2012. 152 s. ISBN 978-80-7204-822-9. (CS)
 JAWLIK, Andrew A. Statistics from A to Z: confusing concepts clarified. Hoboken: Wiley, 2016. ISBN 978-1-119-27203-8. (EN)
NEUBAUER, Jiří; SEDLAČÍK, Marek a KŘÍŽ, Oldřich. Základy statistiky: aplikace v technických a ekonomických oborech. 3., rozšířené vydání. Praha: Grada Publishing, 2021. ISBN 978-80-271-3421-2. (CS)
Studijní materiály dostupné na platformě Moodle. (CS)

Recommended reading

ANDĚL, Jiří. Statistické úlohy, historky a paradoxy. Praha: Matfyzpress, 2018. ISBN 978-80-7378-360-0. (CS)
BIVAND, Roger; PEBESMA, E. J. a GÓMEZ-RUBIO, Virgilio. Applied spatial data analysis with R. 2. vydání. New York: Springer, 2013. ISBN 978-1-4614-7617-7. (EN)
GARETH, James; WITTEN, Daniela; HASTIE, Trevor  a  TIBSHIRANI, Robert. An Introduction to Statistical Learning: With Applications in R. New York: Springer, 2014. ISBN 978-1-4614-7137-0. (EN)
HIRSCH, Robert. Statistical hypothesis testing with Microsoft Office Excel. Cham: Springer, 2022. ISBN 978-3-031-04201-0. (EN)
PIEGORSCH, Walter W.; LEVINE, Richard A; ZHANG, Hao Helen a LEE, Thomas C. M. Computational statistics in data science. Hoboken: Wiley, 2022. ISBN 978-1-119-56107-1. (EN)

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Syllabus

Basic thematic content of the lectures:

1. Introduction to mathematical statistics
2. Processing small data sets
3. Processing large data sets
4. Point and interval parameter estimation
5. Basic parametric tests
6. Goodness-of-fit tests
7. Analysis of variance
8. Correlation analysis
9. Categorical analysis
10. Linear regression models
11. Linearizable regression models
12. Non-linearizable regression models
13. Time series analysis and decomposition

Exercise

26 hours, compulsory

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Syllabus

Basic thematic content of the exercises:

1. Introduction to mathematical statistics
2. Processing small data sets
3. Processing large data sets
4. Point and interval parameter estimation
5. Basic parametric tests
6. Goodness-of-fit tests
7. Analysis of variance
8. Correlation analysis
9. Categorical analysis
10. Linear regression models
11. Linearizable regression models
12. Non-linearizable regression models
13. Time series analysis and decomposition

 

Expertise

  • Students will understand the basic concepts and principles of mathematical statistics and their application in business process management.
  • Students will have an understanding of the processing of small and large data sets, including their visualization and interpretation using the R programming language.
  • Students will be familiar with point and interval parameter estimation, basic parametric and goodness-of-fit tests, and their application in business process optimization.
  • Students will understand the creation and interpretation of linear and nonlinear regression models, as well as time series analysis and decomposition, with an emphasis on practical applications in business processes using R.

Competencies

  • Students will be able to explain the basic concepts and principles of mathematical statistics and their application in business process management.
  • Students will be able to process small and large data sets, including their visualization and interpretation using the R programming language, and apply these skills as a basis for data analysis and business process optimization.
  • Students will be able to perform point and interval parameter estimation, basic parametric tests, and goodness-of-fit tests, all using R, while applying these statistical methods to optimize business processes.
  • Students will be able to create and interpret linear and nonlinear regression models, as well as analyze and decompose time series, with an emphasis on practical applications in business processes using R.

Professional skills

  • Students will learn to use the R programming language to visualize and interpret data sets.
  • Students will learn to perform point and interval parameter estimation, basic parametric tests, and goodness-of-fit tests using R.
  • Students will learn to apply statistical methods to optimize business processes.
  • Students will learn to create and interpret linear and non-linear regression models, as well as analyze and decompose time series using R.

Self-study

54 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Individual preparation for an ending of the course

50 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.