Czech

Not applicable.

Students obtain needed knowledge from probability theory, descriptive statistics and mathematical statistics which will enable them to understand and apply stochastic models of technical phenomena and processes based on these methods.

Rudiments of the differential and integral calculus.

Not applicable.

The course contains lectures that explain basic principles, problems and methodology of the discipline, and exercises that promote the practical knowledge of the subject presented in the lectures.

Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing both written exams and semester assignment acceptance.
Examination: Evaluation based on points obtained for semester assignment (0-12points) and a test (0-88points). The exam test consists of two parts: a practical part (2 tasks from the theory of probability: probability and its properties, random variable, distribution Bi, H, Po, N and discrete random vector; 2 tasks from mathematical statistics: point and interval estimates of parameters, tests of hypotheses of distribution and parameters); a theoretical part (4 tasks related to basic notions, their properties, sense and practical use,and proofs of two theorems); evaluation: each task 0 to 18 points and each theoretical question 0 to 4 points; evaluation according to the total number of points (scoring 0 points for semestral assignment, any practical part task, any theoretical part task means failing the exam): excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).

Random events, field of events, and probability (properties).
Conditioned probability and independent events (properties).
Reliability of systems. Random variable (types, distribution function).
Functional characteristics of discrete and continuous random variables.
Numerical characteristics of discrete and continuous random variables.
Basic discrete distributions A, Bi, H, Po (properties and use).
Basic continuous distributions R, N, E (properties and use).
Random vector, types, functional and numerical characteristics.
Distribution of transformed random variables.
Random sample, sample characteristics (properties, sample from N).
Parameter estimation (point and interval estimates of parameters Bi and N).
Testing statistical hypotheses.
Testing hypotheses of parameters of Bi and N.

Not applicable.

The course makes students familiar with descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameter estimation, tests of hypotheses and statistical software Statistica. Seminars include solving problems and applications related to mechanical engineering.

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Not applicable.

Not applicable.

Hogg R.V., McKean J., Craig, A.T.: Introduction to Mathematical Statistics. Pearson, Cloth. 2013. (EN)
Michálek, J. Matematická statistika pro informatiky. Praha: Státní pedagogické nakladatelství, 1987. (CS)
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York,1977 (EN)
Zvára, K., Štěpán, J.: Pravděpodobnost a matematická statistika. Praha : Matfyzpress, 2002. (CS)

Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
Lamoš, F. - Potocký, R.: Pravdepodobnosť a matematická štatistika. Bratislava : Alfa, 1989.
Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : PLUS, 1994.
Neubauer J., Sedlačík M., Kříž O.: Základy statistiky. Praha: Grada Publishing. 2012.