Course detail

Probability, Statistics and Operations Research

FEKT-MPC-PSOAcad. year: 2025/2026

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

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

Students may be awarded
Up to 40 points for computer exercises (written test 20 points, 4 homework each max. 5 points).
Up to 60 points for the written final exam. The test contains both theoretical and numerical tasks that are used to verify the orientation of students in statistics and operations research. Numerical tasks are included to verify the student's ability to apply statistical and optimization methods in technical and economic practice.
Requirements for successful completion of the are course provided in an annual public notice.

Computer exercises are compulsory. Properly excused absence can be replaced by individual homework, which focuses on the issues discussed during the missed exercise.
Specifications of the controlled activities and ways of implementation are provided in annual public notice.
Date of the written test is announced in agreement with the students at least one week in advance. The new term for properly excused students is usually during the credit week.

Exercises are compulsory. Duly excused absences may be made up by arrangement with the teacher. The form and method of substitution is at the sole discretion of the techer.

Any student who obtains a non-zero number of points for the exercise is admitted to the examination.

To pass the course, a student must score a minimum of 50 points on both the exam and the practicum.

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 hod., optionally

Teacher / Lecturer

Ing. Michal Fusek, 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 hod., compulsory

Teacher / Lecturer

Ing. Michal Fusek, 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.

VUT

Faculties

University Institutes

Parts

Probability, Statistics and Operations Research

Type of course unit