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Lecturer(s)
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Hron Karel, prof. RNDr. Ph.D.
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Fačevicová Kamila, Mgr. Ph.D.
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Vencálek Ondřej, doc. Mgr. Ph.D.
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Course content
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1. Motivation to study probability and mathematical statistics. Random events. 2. Probability, properties of probability, probability models, conditional probability. Bayes theorem. Independent random events. 3. Random variable, probability distribution, distribution function. Discrete and continuous random variables. Probability distribution of function of a random variable. 4. Numerical characteristics of discrete and continuous random variables. 5. Basic probability distributions, practical examples of their usage. 6. Random vector, probability distribution (simultaneous) and distribution function of a random vector, discrete and continuous random vector. Marginal distributions of a random vector, its computation from simultaneous distribution. 7. Independent random variables, properties and mutual relationships with marginal distributions. 8. Conditional distribution, conditional density, Bayes theorem again, conditional expectation and variance. 9. Numerical characteristics of a random vector, their usage for description of distribution of a random vector. 10. Further important continuous probability distributions: chi square, t, F. Weak law of large numbers, classical limit theorems of probability theory, their applications. 11. Introduction to Monte Carlo methods - motivation, pseudorandom numbers, generating values of random variables with a given distribution. 12. Applications of Monte Carlo methods.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
- Attendace
- 65 hours per semester
- Preparation for the Course Credit
- 25 hours per semester
- Homework for Teaching
- 25 hours per semester
- Preparation for the Exam
- 65 hours per semester
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Learning outcomes
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Understand probability theory.
Comprehension Understand the mathematical tools of probability theory.
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Prerequisites
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Basic knowledge of mathematical analysis.
KMA/MA1
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation, the student has to pass written tests after each thematic block. Exam: written and oral.
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Recommended literature
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Budíková, M., Mikoláš, Š., Osecký, P. (2007). Teorie pravděpodobnosti a matematická statistika. Sbírka příkladů. MU, Brno.
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Hogg R. V., McKean, J.W., Craig A.T. (2005). Introduction to mathematical statistics. Prentice Hall, Upper Saddle River.
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Hron K., Kunderová P., Vencálek O. (2018). Základy pravděpodobnosti a metod matematické statistiky. VUP, Olomouc.
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Jarod, J., Protter, P. (2004). Probability essentials (2nd edition). Springer, Heidelberg.
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Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge University Press, Cambridge.
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Zvára, K., Štěpán, J. (2006). Pravděpodobnost a matematická statistika. Matfyzpress, Praha.
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