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Lecturer(s)
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Fačevicová Kamila, Mgr. Ph.D.
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Vencálek Ondřej, doc. Mgr. Ph.D.
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Fišerová Eva, doc. RNDr. Ph.D.
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Hron Karel, prof. RNDr. 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. 3. Independent random events. Random variable, probability distribution, distribution function. 4. Discrete and continuous random variables. Probability distribution of function of a random variable. 5. Numerical characteristics of discrete and continuous random variables. 6. Basic probability distributions, practical examples of their usage. 7. Random vector, probability distribution (simultaneous) and distribution function of a random vector, discrete and continuous random vector. 8. Marginal distributions of a random vector, its computation from simultaneous distribution. 9. Independent random variables, properties and mutual relationships with marginal distributions. Conditional distribution. 10. Numerical characteristics of a random vector, their usage for description of distribution of a random vector. 11. Further important continuous probability distributions: chi square, t, F. Weak law of large numbers, classical limit theorems of probability theory, their applications. 12. Introduction to 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 and descriptive statistics.
Comprehension Understand the mathematical tools of probability theory.
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Prerequisites
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Basic knowledge of mathematical analysis.
KMA/M1N
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to pass three written tests (i.e. at least in two of them at least one whole example correct). Exam: pass written test (at least one whole example out of two correct), the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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Budíková, M., Mikoláš, Š., Osecký, P. (2001). 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. Introduction to mathematical statistics.
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Hron, K., Kunderová, P. (2015). Základy počtu pravděpodobnosti a metod matematické statistiky (2. vydání). VUP, Olomouc.
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Jarod, J., Protter, P. (2004). Probability essentials (2nd edition). Springer, Heidelberg.
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Zvára, K., Štěpán, J. (2006). Pravděpodobnost a matematická statistika. MATFYZPRESS, Praha.
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