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Lecturer(s)
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Picek Jan, prof. RNDr. CSc.
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Volf Petr, doc. CSc.
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Course content
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Random event, definition of probability. Independence of random events, conditional probability, Bayes theorem. Random variable. Probability distribution. Distribution function and its properties. Moment characteristics. Moment-generating function. Quantiles. Examples of discrete probability distribution. Examples of continuous probability distribution. Transformation and function of random variable. Multidimensional random variable (random vector). Covariance and correlation matrices. Some random vectors distributions. Chebyshev's inequality, laws of large numbers, cetral limit theorems. Definition of random sequence and stochastic process. Stationary process. Autocorrelation function. Markov chain and its transition matrix. Time-homogeneous Markov chain. Continuous-time Markov proces. Transition rate matrix. Birth-death proces. Poisson process. Stochastic process with stationary independent increments. Gaussian processes, Brownian motion. Methods for simulation of random variables.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Preparation for exam
- 125 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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Knowledge of advanced methods of probability theory and their understanding, special attention will be given random processes.
Knowledge and ability to apply advanced methods of probability theory and random processes.
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Prerequisites
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Knowledge of differential and integral calculus and the fundamentals of mathematical statistics and probability.
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Assessment methods and criteria
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Oral exam, Written exam
Requirements on credit: two tests of the subject matter. The date of each test will be announced in advance by teacher. It is necessary to get score at least 50% for each test. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
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Recommended literature
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Linka A., Picek J., Volf P. Úvod do teorie pravděpodobnosti.. Liberec: Technická univerzita v Liberci, 2001. ISBN 80-7083-453-6.
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Prášková Z., Lachout P. Základy náhodných procesů. Karolinum Praha, 1998. ISBN 978-80-7378-210-8.
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Štěpán J. Teorie pravděpodobnosti. Praha, 1987.
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