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Lecturer(s)
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Schindler Martin, Mgr. Ph.D.
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Slámová Tereza, Mgr. Ph.D.
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Course content
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1. Combinatorics 2. Probability theory: random events, the definition of probability, probability properties. 3. The independence of random events, conditional probability. Bayes theorem. 4. Descriptive Statistics: Types of variables, basic characteristics of location and variability. Ordered data, median, quantiles. Graphic data processing. 5. Random variable. Distribution function and its properties, density, quantile function. Characteristics of random variables. The law of large numbers. 6. Discrete random variables: alternative, binomial, negative binomial, hypergeometric, Poisson. 7. Continuous distributions: normal distribution, uniform, exponential, Weibull, Student and F distributions. The central limit theorem. 8. Multivariate random variable (vector), the dependence - covariance and correlation coefficient 9. Introduction to Mathematical Statistics. Point and interval estimates. 10. Basic concepts of statistical hypothesis testing. Tests of hypotheses on the parameters of the normal and binomial distribution. 11. One-way analysis of variance. Non-parametric tests. 12. Goodness of fit tests. 13. Correlation and regression. Spearman's coefficient of serial correlation. 14. Linear regression, method of least squares. Regression diagnostics.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 42 hours per semester
- Preparation for exam
- 106 hours per semester
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Learning outcomes
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Elements of probability theory, data analysis and statistics.
Basic knowledge of mathematical statistics and probability
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Prerequisites
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Basic knowledge of differential and integral calculus (first year)
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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 60% for each test. Further, active participation in practice is required. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
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Recommended literature
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Anděl, J. Statistické metody. Matfyzpress: Praha, 2007. ISBN 978-80-7378-003-6.
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Calda E., Dupač, V. Matematika pro gymnázia: kombinatorika, pravděpodobnost a statistika. Praha : Prometheus, 2004. ISBN 80-7196-147-7.
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Kadeřábek, J. - Picek, J. Sbírka příkladů z pravděpodobnosti a statistiky. Liberec : Technická univerzita v Liberci, 2001. ISBN 80-7083-454-4.
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Kadeřábek J. Statistika. Liberec : Technická univerzita v Liberci, 2006. ISBN 80-7372-044-2.
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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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