Course detail

Probability, Statistics and Operations Research

FEKT-MPC-PSOAcad. year: 2026/2027

The course focuses on consolidating and expanding students' knowledge of probability theory, mathematical statistics and theory of selected methods of operations research. Thus it begins with a thorough and correct introduction of probability and its basic properties. Then we define a random variable, its numerical characteristics and distribution. On this basis we then build descriptive statistics and statistical hypothesis testing problem, the choice of the appropriate test and explanation of conclusions and findings of tests. In operational research we discuss linear programming and its geometric and algebraic solutions, transportation and assignment problem, and an overview of the dynamic and probabilistic programming methods and inventories. In this section the illustrative examples are taken primarily from economics.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. Ing. Michal Fusek, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

We require knowledge at the level of bachelor's degree, i.e. students must have proficiency in working with sets (intersection, union, complement), be able to work with matrices, handle the calculation of solving systems of linear algebraic equations using the elimination method and calculation of the matrix inverse, know graphs of elementary functions and methods of their design, differentiate and integrate of basic functions.

Rules for evaluation and completion of the course

Tests during the semester: 30 points (2 tests, each worth max. 15 points).
Final exam: 70 points.
Exam prerequisites: get at least 13 points during the semester.

Aims

The objecive of the course is to enlarge the knowledge in the area of statistical tests and confidence intervals, to show some spheres of mathematical thinking in economics and to introduce the concepts of recursive algorithms.
After completing the course the student will be able to:
• Describe the role of probability using set operations.
• Calculate basic parameters of random variables, both continuous and discrete ones.
• Define basic statistical data.
• List the basic statistical tests.
• Describe the work with statistical tables.
• Select the appropriate method for statistical processing of input data and perform statistical test.
• Explain the nature of linear programming.
• Convert a word problem into the canonical form and solve it using a suitable method.
• Perform sensitivity analysis in a geometric and algebraic way.
• Convert the specified role into its dual.
• Calculate the optimal solution transport tasks and task assignment optimal solution.
• List the different models in stocks reserve.

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)

Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Mgr. Martin Tůma, Ph.D.

Syllabus

1. Probability, random variable, characteristics, limit theorems.

2. Statistics, parameter estimates, t-test.

3. Analysis of diffusion, one-and two-factor.

4. Correlation approach, regression line.

5. After the spread of dispersion and/or the place of it.

6. Splitting " chi-square " and its application.

7. Non-parametric tests.

8. Linear programming, simplex method.

9. Duality in linearing programming.

10. Traffic and assignment task.

11. Dynamic programming.

12. Stock models.

13. Probability dynamic programming.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Mgr. Martin Tůma, Ph.D.

Syllabus

1. Probability, random variable, characteristics, limit theorems
2. Statistics, parameter estimates, t-test
3. Analysis of diffusion, one-and two-factor
4. Correlation approach, regression line
5. After the spread of dispersion and/or the place of it
6. Splitting " chi-square " and its application
7. Non-parametric tests
8. Linear programming, simplex method
9. Duality in linearing programming
10. Traffic and assignment task
11. Dynamic programming
12. Stock models
13. Probability dynamic programming

Regular individual preparation for activities in the semester

26 hours, optionally

Teacher / Lecturer

doc. Ing. Michal Fusek, Ph.D.

Syllabus

Studenti a studentky se pravidelně připravují na cvičení, aby průběžně zvládli probíranou látku, studují výukové podklady z přednášek a ze cvičení.

Individual preparation for a final exam

52 hours, optionally

Teacher / Lecturer

doc. Ing. Michal Fusek, Ph.D.

Syllabus

Samostudium výukových podkladů z přednášek a ze cvičení popř. jiných relevantních zdrojů.

Elearning

eLearning: currently opened course