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Lecturer(s)
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Fišerová Eva, doc. RNDr. Ph.D.
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Course content
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1. Probability measures 2. General measures 3. Outer measure 4. Measure functions 5. Integral and its properties 6. Integral with respect to Lebesgue measure 7. Product measure and Fubini's Theorem 8. Random variables and distributions 9. Expected values 10. Sums of independent random variables 11. The Radon-Nikodym Theorem 12. Conditional probability
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master essential limit theorems of probability theory, relations among convergence of random variables and a general concept of probability density functions.
Knowledge To know limit theorems of probability theory based on the measure theory and theory of integral, relations among convergence of random variables and a general concept of probability density functions.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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Billingsley, P. (2012). Probability and Measure. Wiley, Hoboken.
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M. Loeve. (1963). Probability theory. 3rd edition.. Princeton, N. J.-Toronto- New York-London: D. Van Nostrand Company, Inc.
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P. R. Halmos. (1974). Measure Theory. Springer, New York, etc.
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