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Lecturer(s)
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Javůrek Milan, doc. Ing. CSc.
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Hrůzová Klára, Mgr. Ph.D.
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Marek Jaroslav, Mgr. Ph.D.
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Course content
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Statistics - summary Probability theory. Random events and elementary event space. Probability. Axiomatic, classical, geometrical and statistical definition of probability. Bertrand´s paradox. Conditional probability, independent random events. The complete probability. One-dimensional and multi-dimensional random variable. Continues and discrete random variable. Probability function, probability density function, distribution function. Marginal and conditional distribution. Moments, measures of position and measures of dispersion of one-dimensional and two-dimensional random distribution. Selected distributions of discrete and continuous one-dimensional random variables : two point, binomial, Poisson distribution, uniform, exponential, normal distribution, Chi-square, t, F distribution. Chebyshev theorem, central limit theorem. Statistical methods Population and random sample. Empirical distribution. Sample moments, sample arithmetic mean, sample variation. Estimation methods.Point estimation. Interval estimation. Confidence intervals for expected value and for variance . Lower and upper control limits. Statistical hypothesis testing.A null hypothesis, an alternative hypothesis, the level of significance of the test, the critical region, one-sided tests, two-sided tests. Testing the hypothesis concerning the expected value of the normal distribution, testing the hypothesis concerning the variance of the normal random variable. The u-test, t-test, F-test. Non-parametric hypothesis testing. The sign test, Wilcoxon test. The chi-square test for goodness of fit. The least square method. Linear regression model by the least square method. Testing significance of regression coefficient and intercept. Confidence intervals of regression coefficient and intercept. Correlation. Measures of dependence. Study of significance of correlations.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Skills training, Stimulating activities (simulation, games, drama)
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Learning outcomes
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The goal is to get the students familiar with the fundamental terms of the theory of probability and the principles of statistical data analysis.
Capability of statistical data evaluation and interpretation of results.
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Prerequisites
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Knowledge derivatives and integrals ( one and two variables), basic knowledge of logic and how to work with sets, elementary linear algebra.
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Assessment methods and criteria
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Written examination, Student performance assessment, Work-related product analysis
Requirement: 80% participation + credit test. For a repeating students: Recurring student can choose either a 80% participation and recognition test from last year, or at least 50% attendance and a new credit test. The course is completed by written exam, at least 50% of success is required. An oral form of the exam is optional, upon a student's request.
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Recommended literature
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Anděl, J. Matematická statistika. SNTL&ALFA, Praha, 1978.
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Ayres, F., Mendelson, E. Schaum's Outline of Probability, Random Variables, and Random Processes. Mcgraw-Hill. New York, 2012. ISBN 9780071795531.
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Cyhelský, Lubomír. Elementární statistická analýza. Praha: Management Press, 1996. ISBN 80-85943-18-2.
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Hátle, J., Likeš, J. Základy počtu pravděpodobnosti a matematické statistiky. Praha: SNTL, 1974. ISBN 04-311-74.
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Hsu, H. Schaum's Outline of Probability, Random Variables, and Random Processes. Mcgraw-Hill. New York, 2010. ISBN 9780071632898.
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Kolda,S. Úvod do počtu pravděpodobnosti a matematické statistiky. VŠCHT, Pardubice, 1980.
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Kubanová J. Statistické metody pro ekonomickou a technickou praxi. Statis Bratislava, 2004. ISBN 80-85659-379.
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Kubanová, Jana. Sbírka příkladů z pravděpodobnosti. Bratislava: Statis, 2004. ISBN 80-85659-36-0.
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Kubanová, Jana. Teorie pravděpodobnosti. Pardubice: Univerzita Pardubice, 1999. ISBN 80-7194-193-X.
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