Course Unit Code | 470-2405/01 |
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Number of ECTS Credits Allocated | 7 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | Second Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| KRA0220 | Ing. Jan Kracík, Ph.D. |
Summary |
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Probability theory provides a framework for treating uncertainty and is a foundation for mathematical statistics. Students will gain knowledge of fundamental notions of probability theory at a level not requiring knowledge of measure theory. |
Learning Outcomes of the Course Unit |
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Students will understand basic concepts and relations in probability theory needed for mathematical statistics. |
Course Contents |
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Lectures:
Probability space
Conditional probability, independent random events, law of total probability, Bayes' theorem
Conditional independence of random events
Random variable, probability distribution, numerical characteristics
Selected discrete distributions
Selected continuous distributions
Multivariate random variable, probability distribution, numerical characteristics
Independece of random variables, conditional independence
Multivariate normal distribution
Convergence of random variables
Limit theorems
Transformations of random variables, sum of random variables, sampling
Excercises will follow the content of the lectures. During the excercises students will learn basics of R language.
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Recommended or Required Reading |
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Required Reading: |
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RAO, C. RADHAKRISHNA. Linear statistical inference and its applications. 2. ed., paperback ed. New York: Wiley, 2002. ISBN 0471218758. |
ANDĚL, Jiří. Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1985.
RAO, C. RADHAKRISHNA. Linear statistical inference and its applications. 2. ed., paperback ed. New York: Wiley, 2002. ISBN 0471218758. |
Recommended Reading: |
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TEETOR, Paul. R cookbook. Sebastopol, CA: O'Reilly, 2011. ISBN 9780596809157
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TEETOR, Paul. R cookbook. Sebastopol, CA: O'Reilly, 2011. ISBN 9780596809157
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Planned learning activities and teaching methods |
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Lectures, Tutorials, Project work |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 30 | 10 |
Examination | Examination | 70 | 35 |