Course: Applied Mathematical Statistics

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Course title Applied Mathematical Statistics
Course code KMA/MSTA
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Vencálek Ondřej, Mgr. Ph.D.
  • Hron Karel, doc. RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
  • Preparation for the Exam - 40 hours per semester
  • Attendace - 52 hours per semester
Learning outcomes
Understand basics of probability theory and mathematical statistics and their applications in physics.
Application Apply methods of probability theory and mathematical statistics in physics.
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria
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. Exam: the student has to understand the subject.
Recommended literature
  • A. C. Rencher. (2000). Linear models in statistics. John Wiley & Sons Inc. New York.
  • Kubáčková, L. (1990). Metódy spracovania experimentálnych údajov. Veda, Bratislava.
  • Kubáčková, L. (2002). Užitá statistika pro aplikovanou fyziku. Skriptum UP, Olomouc.
  • M. Budíková, T. Lerch, Š. Mikoláš. (2005). Základní statistické metody. Brno, skriptum PřF MU.
  • P. Kunderová. (2004). Úvod do teorie pravděpodobnosti a matematické statistiky (2. vydání). UP Olomouc.
  • R. V. Hogg, A. Craiq, J. Mckean. (2004). Introduction to mathematical statistics. Prentice Hall.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Molecular Biophysics (2015) Physics courses 3 Winter
Faculty of Science Biophysics (2015) Physics courses 3 Winter
Faculty of Science Optics and Optoelectronics (1) Physics courses 3 Winter
Faculty of Science General Physics and Mathematical Physics (1) Physics courses 3 Winter
Faculty of Science Applied Physics (1) Physics courses 3 Winter