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Lecturer(s)
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Štětina Petr, RNDr.
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Kroupa Matěj, Mgr. Ph.D.
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Brada Roman, Ing. Ph.D.
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Dostal Rostislav, Ing. Ph.D.
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Slupská Petra, RNDr. Ph.D.
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Course content
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1. Events in probability spaces, definitions of probability. 2. Conditional probabilities, Bayes?s theorem, independent events. 3. Random variable. Probability density function. Distribution function. Parameters of a distribution. Mathematical expectation and moments. 4. List of important discrete distributions. 5. List of important continuous distributions. 6. Normal (Gaussian) distribution. Central limit theorem. 7. Random vector. Correlation and covariance. 8. Collection of statistical data, principles of descriptive statistics. 9. Inferential statistics (point and interval estimation), confidence intervals. 10. Statistical hypothesis testing. Null and alternative hypothesis. Rejection and acceptance region. P-value of the statistical test. 11. Chi-square goodness of fit test. Contingency tables. Tests of independent. 12. Regression analysis.
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Learning activities and teaching methods
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Lecture with practical applications, Collaborative instruction, Cooperative instruction
- Preparation for formative assessments (2-20)
- 30 hours per semester
- Contact hours
- 26 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| to use the principles of the differential and integral calculus |
| to formulate fundamental combinatorial reasoning |
| to interpret the geometrical meaning of definite integral |
| Skills |
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| to use basic real functions |
| to calculate derivations and integrals |
| to calculate the sum of geometrical series |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| basic types of statistical distributions |
| principles of the statistical hypothesisi |
| correlation and regression analyses |
| Skills |
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| to calculate probability based on combinatorial approac |
| to find suitable mathematical models of probability distribution for real data |
| to calculate the probability for selected discrete and continuous distribution |
| to calculate confidence intervals for parameters of normal distribution |
| to use at least two different statistical tests on real model problems and interpret the results |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Practicum |
| Task-based study method |
| Skills |
|---|
| Practicum |
| Task-based study method |
| Competences |
|---|
| Practicum |
| Task-based study method |
| assessment methods |
|---|
| Knowledge |
|---|
| Test |
| Skills |
|---|
| Test |
| Skills demonstration during practicum |
| Competences |
|---|
| Test |
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Recommended literature
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Ayyub, Bilal M.; McCuen, Richard H. Probability, statistics, and reliability for engineers and scientists. Third edition. 2011. ISBN 978-1-4398-0951-8.
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Brousek, Jan; Ryjáček, Zdeněk. Sbírka řešených příkladů z počtu pravděpodobnosti. 1. vyd. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-063-2.
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Devore, Jay L. Probability and statistics for engineering and the sciences. Boston, MA: Brooks/Cole, Cengage Learning, 2012. ISBN 978-0-538-73352-6.
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Likeš, Jiří; Machek, Josef. Počet pravděpodobnosti. 2. vyd. Praha : SNTL, 1987.
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Reif, J. Metody matematické statistiky. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-302-7.
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Reif, Jiří; Kobeda, Zdeněk. Úvod do pravděpodobnosti a spolehlivosti. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-702-5.
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