| Course title | Probability and mathematical statistics I |
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| Course code | UMB/737 |
| Organizational form of instruction | Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 3 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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Course content: 1. The concept of chance, probability and its various definitions, combinatorics. 2. Conditional probability, independence of events. 3. The law of total probability, Bayes' formula, applications in diagnostics. 4. Random variables, discrete and continuous random variables, distribution of random variables. 5. Characteristics of random variables, generation of random numbers. 6. Random vector, joint and marginal distributions, covariance and correlation. 7. Parameter estimation, maximum likelihood method, confidence intervals 8. Fundamentals of statistical testing: introductory motivational example, general principles 9. Fundamentals of statistical testing: most common specific tests 10. Contingency tables 11. ANOVA 12. Linear and nonlinear regression
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
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| Learning outcomes |
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Introduce and explain the basics of probability and mathematical statistics. The aim is not only to teach students how to calculate in the presence of randomness, but also to offer an understanding of the principles of comprehending uncertainty and working with it, how to think in such situations, what principles individual procedures are based on, to offer insight and orientation in this issue, and thus facilitate the understanding of specific calculation procedures.
Ability to explain the concept of chance, the basic principles of reasoning when chance is involved. Ability to calculate basic probability problems and understand the practical application of probability. Understanding of basic statistical methods. |
| Prerequisites |
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Mathematics knowledge within the scope of the UMB/010 course.
UMB/CV010 ----- or ----- UMB/CV564 ----- or ----- UMB/010 ----- or ----- UMB/564 |
| Assessment methods and criteria |
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Written examination, Interim evaluation
To complete the course, students must obtain a credit and pass the exam. To obtain a credit, students must attend a sufficient number of classes and achieve a sufficient average score (50%) on the homework assignments. A credit is a prerequisite for taking the exam. The exam is written and is passed with a score of 50% or higher. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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