1. Random events, sample space, algebra of random events 2. Definition of probability: classical, geometric, statistical, axiomatic (Kolmogorov) 3. Conditional probability, independence of random events, independent repetitions of a partial trial 4. Complete systems of random events and probability distribution 5. Random variable (discrete, continuous, general), distribution function, probability density 6. Random vector, distribution function, two-dimensional random vectors, marginal distribution, independence 7. Functions of random variables and their distribution, distribution of sum, product and quotient of random variables 8. Numerical characteristics of random variables, general and central moments, characteristic function 9. Convergence of random variables, central limit theorem, laws of large numbers, Chebyshev's inequality 10. Numerical characteristics of random vectors Tutorial 1. Combinatorics 2. Random event, definition of probability, conditional and complete probability, Bayes formula 3. Random variable, distribution of random variable, characteristics of random variable 4. Examples of discrete and continuous distributions, important continuous distributions (central limit theorem) 5. Principles of statistical testing, chi-2 tests 6. t-tests 7. ANOVA 8. Correlation and regression
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Mrkvička T., Petrášková V. Úvod do statistiky, Jihočeská univerzita. 2006. ISBN 80-7040-894-4.
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Petrášková V., Tlustý P. Úvod do počtu pravděpodobnosti. 2006. ISBN 978-80-7394-115-4.
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