## MU20009 Probability and Statistics I

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Oldřich Stolín, Ph.D. (lecturer)
Mgr. Vojtěch Pravec, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
Timetable
Wed 15:35–17:10 BF - BrainFitness
• Timetable of Seminar Groups:
MU20009/01: Thu 14:45–16:20 BF - BrainFitness, V. Pravec
Prerequisites (in Czech)
MU20002 Mathematical Analysis II && TYP_STUDIA ( B )
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main goal of this two-semestral course is to introduce the fundamental notions and principles of probability theory and mathematical statistics. The first part of the course is devoted to the explanation of the fundamentals of probability theory and its relation to mathematical statistics.
Syllabus
• 1. Probability: classical definition and its generalizations, axiomatic definition of probability, selected probability models, conditional probability and independence, Bayes' formula.
2. Random variable and its distribution function: Borel functions, continuity of the probability from above and from below, definition of a random variable, definition of distribution functions and their main properties, definition of probability distribution.
3. Numerical characteristics of random variables: expected value, Lebesgue-Stieltjes measure derived from a distribution function, density function of a random variable, variance, moments, discrete and continuous random variables.
4. Selected probability distributions and their properties.
5. Random vectors, independence and uncorrelation of random variables, conditional expected value.
6. Central limit theorem.
7. Introduction to the theory of stochastic processes.
Literature
required literature
• K. Zvára, J. Štěpán. Pravděpodobnost a matematická statistika. Praha, 2012. ISBN 978-80-7378-218-4. info
• S.Dineen. Probability Theory in Finance: A Mahematical Guide to the Black-Sholes Formula. 2005. ISBN 0-8218-3951-9. info
• Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
recommended literature
• T. Neubrunn, B. Riečan. Miera a integrál. Bratislava, 1981. info
not specified
• J. Anděl. Matematika náhody. Matfyzpress, Praha, 2000. ISBN 80-85863-52-9. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The final exam consists of a written (at least 60%) and an oral part (2 theoretical questions). To obtain the pre-exam credits it is neccessary to actively participate in seminars on a regular basis and passing two written tests (60% at least).

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