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Lecturer(s)
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Vencálek Ondřej, doc. Mgr. Ph.D.
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Hron Karel, prof. RNDr. Ph.D.
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Fačevicová Kamila, Mgr. Ph.D.
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Course content
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1. Introduction to probability. 2. Random variables and random vectors, distribution functions, characteristics of random variables. 3. Selected probability distributions. 4. Sample, population, scale types. Point and interval frequencies distribution. 5. Empirical distribution function, empirical characteristics. 6. Histogram, Box-and-whisker plot. 7. Random sample from normal distribution. 8. Basic models of measurement, linearization. 9. Estimator of the mean value parameters and of the unit dispersion. 10. Estimator of the covariance matrix in replicated models. 11. Confidence ellipsoids. 12. Introduction to hypotheses testing. 13. Testing parameters of the normal distribution. 14. Hypotheses testing in linear models. 15. Tests on outliers.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
- Preparation for the Exam
- 40 hours per semester
- Attendace
- 52 hours per semester
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Learning outcomes
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Understand basics of probability theory and mathematical statistics and their applications in physics.
Application Apply methods of probability theory and mathematical statistics in physics.
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Prerequisites
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Basic knowledge of mathematical analysis and linear algebra.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to pass a written test and to obtain at least half of the possible points. Write a course work. Active participation. Exam: the student has to understand the subject.
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Recommended literature
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A. C. Rencher. (2000). Linear models in statistics. John Wiley & Sons Inc. New York.
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Hron, K., Kunderová, P. (2015). Základy počtu pravděpodobnosti a metod matematické statistiky (2. vydání). VUP, Olomouc.
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Kubáčková, L. (1990). Metódy spracovania experimentálnych údajov. Veda, Bratislava.
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Kubáčková, L. (2002). Užitá statistika pro aplikovanou fyziku. Skriptum UP, Olomouc.
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M. Budíková, T. Lerch, Š. Mikoláš. (2005). Základní statistické metody. Brno, skriptum PřF MU.
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R. V. Hogg, A. Craiq, J. Mckean. (2004). Introduction to mathematical statistics. Prentice Hall.
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