### Course: Statistical Evaluation of Experimental Data for Combined Studies

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 Course title Statistical Evaluation of Experimental Data for Combined Studies UFY/SVEK Lecture + Lesson Bachelor not specified In each academic year, in the winter semester. Winter 5 Czech Compulsory Face-to-face This is not an internship None
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), E-learning, 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.

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.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Measuring and Computer Technology (1) Category: Electrical engineering, telecommunication and IT 2 Recommended year of study:2, Recommended semester: Winter