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Lecturer(s)
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Slavíček Ondřej, Mgr. Ph.D.
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Linda Bohdan, doc. RNDr. CSc.
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Kubanová Jana, doc. PaedDr. CSc.
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Zapletal David, Mgr. Ph.D.
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Brebera David, Mgr.
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Pacáková Viera, prof. RNDr. Ph.D.
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Course content
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Random variable, probability distribution, distribution function The basic characteristics of one-dimensional and multidimensional random variables, measure of independence (expected value, variance, covariance, correlation coefficient) Common probability distributions, important for economical applications. Random sample and its classification, sample characteristics, quantiles. Empirical probability distribution Parameters estimation, point estimates, method of moments, method of maximal likelihood. Probability distribution of some sample characteristics. Confidence intervals for expected value and for variance. Hypothesis testing, significance testing for expected values and for variance. Good fitness test, Chi square test. Kolmogorov-Smirnov test, Lilliefors test. Nonparametric tests, sign test, Wilcoxon's test, outlier test, independence test and other. Regression analysis, linear regression, least squares method. Linear regression model for the function y = a+bf(x). Correlation analysis, Pearson´s and Spearman's correlation coefficient.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
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Learning outcomes
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The goal of course is to create students theoretical foundations for related subjects, especially Statistical inference, Statistical methods in economics and other disciplines based on theory of stochastic processes.
Students will be able to apply methods of the probability theory in encountering practical tasks as well as in real situations.
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Prerequisites
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Prerequisite for mastering of the subject PPAS1 is knowledge of the subjects mathematics 1 and mathematics 2.
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Assessment methods and criteria
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Home assignment evaluation, Student performance assessment, Systematic monitoring
Assignment-completion of all given tasks and passing all written tests. The exam consists of two parts - practical (counting of examples) and theoretical (demonstration of knowledge of the used terminology and understanding of used methods). Pass the exam involves acquiring at least 65% in each (practical and theoretical). If the student omits substantial part of the subject matter will be evaluated fail even if obtains more than 65% points in any part.
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Recommended literature
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Gibilisco, Stan. Statistics demystified : [a self-teaching guide]. New York: McGraw-Hill, 2004. ISBN 0-07-143118-7.
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Kubanová, Jana. Probability. Pardubice: Univerzita Pardubice, 2007. ISBN 978-80-7194-934-3.
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Kubanová, Jana. Sbírka příkladů z pravděpodobnosti. Bratislava: Statis, 2004. ISBN 80-85659-36-0.
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Kubanová, Jana. Statistické metody pro ekonomickou a technickou praxi. Bratislava: Statis, 2008. ISBN 978-80-85659-47-4.
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Kubanová, Jana. Teorie pravděpodobnosti. Pardubice: Univerzita Pardubice, 1999. ISBN 80-7194-193-X.
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Linda, Bohdan. Pravděpodobnost. Pardubice: Univerzita Pardubice, 2010. ISBN 978-80-7395-303-4.
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Linda,B.-Kubanová,J. Kritické hodnoty a kvantily vybraných rozdělení pravděpodobnosti. Univerzita Pardubice, 2006. ISBN 80-7194-852-7.
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Mendehall, W. - Sincich, T. Statistics for Engineering and Sciences. New York, Macmillan Publishing Company 1992, 1992. ISBN 002946563X.
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Milton, J. S., Arnold, J. Introduction to probability and statistics. New York, McGraw-Hill 2002, 2002.
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Selvin,S. Biostatistics: How it works. Pearson Education, Prentice-Hall 2004, 2004. ISBN 0-138-046616-.
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Spiegel, M. R. Theory and Problems of Probability and Statistics. Singapore, McGraws-Hill Book 1985, 1985. ISBN 007990301.
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