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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
- Tests during the semester: 30 points (3 tests, each worth max. 10 points).
- Final exam: 70 points.
- Exam prerequisites: get at least 10 points during the semester.
Aims
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
Prerequisites and corequisites
Basic literature
BAŠTINEC, J., FAJMON, B., KOLÁČEK, J., Pravděpodobnost, statistika a operační výzkum. Brno 2014. 360 stran. (CS)
Recommended reading
Elearning
Classification of course in study plans
- Programme MPC-NCP Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-AUD Master's
specialization AUDM-TECH , 1 year of study, winter semester, compulsory-optional
specialization AUDM-ZVUK , 1 year of study, winter semester, compulsory-optional - Programme MPC-BIO Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-EAK Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-EEN Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-EKT Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-EVM Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-KAM Master's 1 year of study, winter semester, compulsory
- Programme MPC-MEL Master's 1 year of study, winter semester, compulsory-optional
- Programme MPC-SVE Master's 0 year of study, winter semester, elective
- Programme MPC-TIT Master's 1 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
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.
Elearning