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Lecturer(s)
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Pavlů Ivana, Mgr. Ph.D.
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Fišerová Eva, doc. 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. Probability theory: Random events, definition of probability, probability spaces. Conditional probability, dependence and independence of random events, total probability, the Bayes formula. Random variables on discrete spaces, independence of random variables, basic moments, characteristic functions. Bernoulli trials, the binomial, Poisson's and multinomial distributions. Random variables on a general space, probability density and probability distribution properties. Normal distribution, exponential distribution, Random vector, probability distribution (simultaneous) and distribution function of a random vector, discrete and continuous random vector. Marginal distributions. Independent random variablesOther important absolutely continuous distributions - Chi-squared distribution, t-distribution, F-distribution. The law of large numbers. The central limit theorems. 2. Mathematical statistics: Descriptive statistics. Random samples, general empirical characteristics and their properties. Estimation of parameters of probability distributions. Statistical testing, construction of statistical tests. Basic statistical methods for analysis of one variable and evaluation of the relationship between variables.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Deepen knowledges in probability theory and mathematical statistics.
Analysis Students analyse the experimental data using the knowledges of the probability theory and the mathematical statistic
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Prerequisites
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Basic knowledge of mathematical analysis.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation in seminars, the student has to turn in individual homework and pass a written test Exam: the student has to understand the subject and be able to use the theory in applications.
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Recommended literature
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Anděl J. (2005). Základy matematické statistiky. MATFYZPRESS, Praha.
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Hron K. , Kunderová P. (2015). Základy počtu pravděpodobnosti a metod matematické statistiky. UP Olomouc.
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Hron, K., Kunderová, P., Vencálek, O. (2018). Základy počtu pravděpodobnosti a metod matematické statistiky. UP Olomouc.
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Zvára K. ,Štěpán J. Pravděpodobnost a matematická statistika. MATFYZPRESS, Praha.
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