Lecturer(s)


Course content

Content of lectures: 1. Definition of probability  classical, statistical, axiomatic 2. Conditional probability and Bayer pattern 3. Random variable, distribution and the frequency function 4. The probability density, statistical moments, the central limit theorem 5. Binomial, Poisson, uniform, Gaussian probability distribution 6. Correlation function, covariance, power spectral density, Wiener Khinchin theorem 7. Composite statistical systems 8. Random vector, its description and the description of its distribution, joint distribution function 9. Statistics  statistical files, basic concepts 10. Statistical ensemble with one argument  the basic characteristics 11. Processing of a large statistical ensemble 12. Correlation and regression  the least squares method, linear and nonlinear regression 13. Parameters estimation of the ensemble  point and interval estimates of the parameters of the basic ensemble. 14. Testing of statistical hypotheses  hypotheses about the variance, mean value. Goodness of fit test and the test of extreme values. Content of practicals: Statistical methods will be used on examples of various physical problems (Brownian motion, power spectral density, temperature fluctuations, electronic noise, etc.)

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Work with text (with textbook, with book), Elearning, Individual preparation for exam, Group work
 Class attendance
 40 hours per semester
 Preparation for classes
 40 hours per semester
 Preparation for exam
 22 hours per semester

Learning outcomes

To acquaint students with basic concepts of probability theory and mathematical statistics. Probability definitions, continuous and discrete random variables, discrete and continuous probability distributions and distribution functions will be discussed. Students will also learn the law of large numbers or the central limit theorem. The course will also focus on describing estimation functions and their properties, displaying random data or constructing confidence intervals. The topics discussed will be practiced on interesting examples.
The graduate gains an overview of the basics of probability theory and mathematical statistics. Based on this knowledge he/she will be able to solve problems in the field of probability and statistics. When working with software tools, they will have an idea of the statistical analyzes provided by these modern software tools. They will apply their knowledge in practice, eg when analyzing the results of experiments.

Prerequisites

Knowledge of the basics of mathematical analysis, as taught in the first two semesters at the University.
UMB/564 and UMB/565

Assessment methods and criteria

Oral examination
Active mastering of the curriculum in the range of lectures given by the thematic plan of the course. Credit: attendance at seminars and active participation in calculating examples. Examination: demonstration of knowledge at the minimum of 75%. During the oral exam, the student will be asked one question from the theory of probability and one question from mathematical statistics.

Recommended literature


Hebák, P., Kahounová, J.: Počet pravděpodobnosti v příkladech. SNTL Praha, 1988.

Meloun, M., Militký, J.: Kompendium statistického zpracování dat, Academia Praha, 2006.

Meloun, M., Militký, J.: Statistická analýza experimentálních dat, Academia Praha, 2004.

Pavelka, L., Doležalová, J.: Pravděpodobnost a statistika, Vysoká škola báňská  Technická Univerzita Ostrava, 1995.

Reisenauer, R.: Metody matematické statistiky a jejich aplikace v technice, SNTL Praha, 1970.

Dekking, F.M., Kraaikamp, C., Lopuhaä, H.P., Meester, L.E. A Modern Introduction to Probability and Statistics. London, 2005. ISBN 1852338962.
