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Lecturer(s)
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Heckenbergerová Jana, Mgr. Ph.D.
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Course content
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Random experiment, axiomatic and classical definition of probability. Properties of probability , conditional probability, independent events, total probability formula,, Bayes' formula. Random variable, probability distribution of a random variable, characteristics of random variables. Selected probability distributions, two-dimensional random variable. Stochastic dependence, regression function. Population, probability distribution of population, random sample, characteristics of random sample, probability distribution of selected characteristics. Estimates of the characteristics of the population - point and interval estimates. Hypothesis testing, principles, one-sample and two-sample tests on expected values and variances. Chi- square test, contingency tables, independence test. Nonparametric tests, tests of outliers. Simple model of linear regression, criteria for selection of regression function, linearizable models. Correlation analysis, Pearson's correlation coefficient, Spearman's correlation coefficient, their tests. Time series, types, cleaning of time series, characteristics of time series. Trend determination of time series, moving averages, trend functions.
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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)
- Contact teaching
- 52 hours per semester
- Preparation for a credit (assessment)
- 10 hours per semester
- Home preparation for classes
- 10 hours per semester
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Learning outcomes
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The aim of the course is to teach the student the basics of probability theory and inductive statistics.
A student who has successfully completed the course can: describe real processes using random variables; understand the nature of the above basic statistical methods. A student who has successfully completed the course can: evaluate statistical investigations; correctly apply the statistical methods discussed; interpret the results of these methods. A student who has successfully completed the course is able to: reason in terms of stochastic calculus and inductive statistics; communicate clearly and convincingly the information arising from the results of statistical analyses.
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Prerequisites
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The prerequisite for mastering the subject is knowledge of mathematics within the scope of the subject Mathematics.
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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 the written test Examination - written work consisting of problems and theoretical part
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Recommended literature
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GIBILISCO, Stan. Statistics demystified: [a self-teaching guide]. New York, 2004. ISBN 0-07-143118-7.
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MENDENHALL, William; BEAVER, Robert J a BEAVER, Barbara M. Introduction to probability and statistics. Belmont, 2006. ISBN 0-534-41870-8.
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NEWBOLD, Paul; CARLSON, William L. a THORNE, Betty M. Statistics for business and economics. Harlow: England, 2023. ISBN 978-1-292-43684-5.
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SPIEGEL, Murray R. a STEPHENS, Larry J. Statistics. New York, 2014. ISBN 978-0-07-182252-7.
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SPIEGEL, Murray R.; SCHILLER, John J. a SRINIVASAN, R. Alu. Probability and statistics. New York, 2013. ISBN 978-0-07-179557-9.
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