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Lecturer(s)
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Urbánek Tomáš, Ing. Ph.D.
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Course content
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- Introduction to the course, fundamental principles of combinatorics - Fundamentals of probability theory and operations with events - Conditional probability and independence of events - Introduction to random variables and their general properties - Discrete random variables and selected probability distributions - Continuous random variables and probability density - Characteristics of random variables, expected value and variance - Fundamentals of descriptive statistics and exploratory data analysis - Relationship between population and sample, principles of statistical surveying - Estimation theory and point estimates of parameters - Method of moments (MoM) for estimating distribution parameters - Advanced topics in applied statistics and course summary
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Learning activities and teaching methods
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Lecturing
- Preparation for examination
- 40 hours per semester
- Home preparation for classes
- 65 hours per semester
- Preparation for course credit
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| Fundamental knowledge of high school mathematics, summation principles, and basic differential and integral calculus of functions of one variable. |
| Fundamental knowledge of high school mathematics, summation principles, and basic differential and integral calculus of functions of one variable. |
| Skills |
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| Ability to perform basic algebraic operations, work with sets, and calculate simple derivatives and integrals of functions. |
| Ability to perform basic algebraic operations, work with sets, and calculate simple derivatives and integrals of functions. |
| learning outcomes |
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| Knowledge |
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| define basic concepts of combinatorics and the axiomatic definition of probability |
| define basic concepts of combinatorics and the axiomatic definition of probability |
| describe the characteristics of discrete and continuous random variables and their distributions |
| describe the characteristics of discrete and continuous random variables and their distributions |
| explain the principles of descriptive statistics and the difference between a population and a sample |
| explain the principles of descriptive statistics and the difference between a population and a sample |
| clarify the essence of point estimates and the method of moments (MoM) |
| clarify the essence of point estimates and the method of moments (MoM) |
| Skills |
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| Calculate the probability of compound events using combinatorial rules |
| Calculate the probability of compound events using combinatorial rules |
| determine numerical characteristics of random variables, such as expected value and variance |
| determine numerical characteristics of random variables, such as expected value and variance |
| process a data set using descriptive statistics methods and interpret the obtained results |
| process a data set using descriptive statistics methods and interpret the obtained results |
| apply point estimates of distribution parameters to data sets |
| apply point estimates of distribution parameters to data sets |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| Practice exercises |
| Practice exercises |
| Skills |
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| Practice exercises |
| Practice exercises |
| Lecturing |
| Lecturing |
| assessment methods |
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| Knowledge |
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| Analysis of the student's performance |
| Analysis of the student's performance |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
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Recommended literature
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NEUBAUER, J., SEDLAČÍK, M., KŘÍŽ, O. Základy statistiky. Aplikace v technických a ekonomických oborech. 2. roz. vyd.. Praha: Grada, 2016. ISBN 978-80-247-5786-5.
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ROSS, Sheldon M. a Erol A. PEKÖZ. A second course in probability. Second edition. Cambridge, United Kingdom. 2023.
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ROSS, Sheldon M. Introduction to probability models. 13th ed. Burlington, Mass. 2023.
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URDAN, Timothy C. Statistics in plain English. Fifth edition. New York. 2022.
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ZVÁRA, K., ŠTĚPÁN, J. Pravděpodobnost a matematická statistika. 6. vyd.. Praha: Matfyzpress, 2019. ISBN 978-80-7378-388-.
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