Probability, Statistics and Operations Research
FEKT-MPC-PSOAcad. year: 2021/2022
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.
Learning outcomes of the course unit
• 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.
Recommended optional programme components
BAŠTINEC, J., MPSO sbírka příkladů, Brbo 2016, 110 stran (CS)
Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for engineers. 6th Edition. John Wiley \& Sons, Inc., New York 2015.ISBN-13: 978-1118539712. (EN)
LOFTUS, J., LOFTUS, E., Essence of Statistics. Second Edition. Alfred A.Knopf, New York 1988. (EN)
TAHA, H.A., Operations research. An introduction. Fourth Edition. Macmilan Publishing Company, New York 1989. (EN)
DEVORE, J.L., Probability ans Statistics for Engineering and the Sciences, 8th edition, ISE, ISBN 978-0-8400-6827-9 (EN)
FREUND, J.E., WILSON, W.J., MOHR, D. L., Statistical methods, 3rd edition, Elsevir, 2010, ISBN 978-0-12-374970-3 (EN)
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
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.
Language of instruction
2. Discrete and continuous distributions of random variables. Properties of the normal distribution. Limit theorems.
3. Statistics. Selection. Statistical processing of the material. Basic parameters and characteristics of the population selection.
4. Basic point and interval estimates. t-test, F-test. The confidence intervals.
5. Linear regression. Post-hoc tests. Goodness.
6. Analysis of variance.
7. Paired test, unpaired test.
8. Non-parametric tests.
9. Operations Research. Linear programming. Graphic solution. Simplex method.
10. Dual role. The sensitivity analysis.
11. The economic interpretation of linear programming.
12. Transport role. Assignment task.
13. Dynamic programming, recursive algorithms, models in stocks reserve.
Specification of controlled education, way of implementation and compensation for absences
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.
Classification of course in study plans
- Programme MPC-SVE Master's, any year of study, winter semester, 5 credits, elective
- Programme MPC-AUD Master's
specialization AUDM-ZVUK , 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-BIO Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-TIT Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-KAM Master's, 1. year of study, winter semester, 5 credits, compulsory
- Programme MPC-EVM Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-EEN Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-EKT Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-MEL Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-EAK Master's, 1. year of study, winter semester, 5 credits, compulsory-optional
- Programme MPC-AUD Master's
specialization AUDM-TECH , 2. year of study, winter semester, 5 credits, compulsory-optional