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Basic lecture on Probability and Statistics for students of computer science. Students will learn the basic methods
and concepts of the probabilistic description of reality: probability, random variable, distribution function and its
density, random vectors, laws of large numbers. The emphasis will be on understanding the principles and the
ability to use them.
Students will also learn the basics of mathematical statistics with an emphasis on
understanding the applicability and on practical usage using the R language.
Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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The students will learn basics of the probability theory and mathematical statistics. The will be able to understand the core of stochastic procedures presented in other courses. Last update: G_M (05.06.2008)
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The credit will be given for active participation in tutorials, quizzes, homework, and successful completion of tests (the exact weight of each of these criteria is determined by the TA).
The nature of the first two requirements does not make it possible for repeated attempts for the credit. The teacher can, however, determine alternative conditions for replacing the missing requirements.
The exam will be semi-oral. Obtaining the credit is necessary before the final exam. Last update: Feldmann Andreas Emil, doc., Dr. (09.02.2022)
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R. Bartoszynski, M. Niewiadomska-Budaj: Probability and Statistical Inference, J. Wiley, 1996. Mor Harchol-Balter: Introduction to Probability for Computing, Cambridge University Press, 2023. G. Grimmett, D. Welsh: Probability - an introduction, Oxford University Press, 2014. M. Mitzenmacher, E. Upfal: Probability and Computing, Cambridge, 2005. S. Ross: A first course in probability, Pearson Prentice Hall, 2010.
J. Anděl: Statistické metody, Matfyzpress, Praha 1998. D. Jarušková: Matematická statistika, skriptum ČVUT, Praha 2000. K. Zvára, J. Štěpán: Pravděpodobnost a matematická statistika, Matfyzpress, Praha 1997. Last update: Šámal Robert, doc. Mgr., Ph.D. (30.09.2024)
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Lecture+exercises. Last update: G_M (29.05.2008)
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The exam is semi-oral, which means that each student will get some questions about to the content of the lecture. After getting some time to prepare, each student will explain their answers to the teacher and the grade is determined by their performance. Each student will get questions on each of the two parts of the lecture (probability theory and statistics).
In exceptional cases the exam can be taken online. Last update: Feldmann Andreas Emil, doc., Dr. (09.02.2022)
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Probability: Axioms of probability, basic examples (discrete and continuous). Conditional probability, the law of total probability, Bayes' theorem. Random discrete variables: expectation, variance, linearity of expectation and its use. Basic discrete distributions. Continuous random variables: description using probability density function. Basic continuous distributions. Independent random variables. Random vectors (marginal distribution). Covariance, correlation. Laws of large numbers, basic inequalities (Markov, Chebyshev, Chernoff), Central limit theorem.
Statistics: Point estimates: unbiased estimates, confidence intervals. Hypothesis testing, significance level. Two-sample tests. Test of goodness of fit, test of independence. Nonparametric estimates. Bayesian and Frequentists Approach. Maximum a posteriori method, Least mean square estimate. Maximum-likelihood method. Bootstrap resampling.
Simulation, generation of random variables from a distribution. Monte Carlo simulation. Informatively: Markov chains. Last update: Šámal Robert, doc. Mgr., Ph.D. (27.01.2022)
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Knowledge required before enrollment: combinatorics, basic formulas calculus (sequences, series, integrals) Last update: Hlubinka Daniel, doc. RNDr., Ph.D. (10.05.2018)
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