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# Course detail

## Mathematics IV

Course unit code: FSI-4M
Type of course unit: compulsory
Level of course unit: Bachelor's (1st cycle)
Year of study: 1, 2
Semester: summer
Number of ECTS credits:
 Learning outcomes of the course unit: Students obtain the needed knowledge of the probability theory, descriptive statistics and mathematical statistics, which will enable them to understand and apply stochastic models of technical phenomena based upon these methods.
 Mode of delivery: 90 % face-to-face, 10 % distance learning
 Prerequisites: Rudiments of the differential and integral calculus.
 Co-requisites: Not applicable.
 Recommended optional programme components: Not applicable.
 Course contents (annotation): The course makes students familiar with descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameters estimation, tests of hypotheses, and linear regression analysis. Seminars include solving problems and applications related to mechanical engineering. PC support is dealt with in the course entitled Statistical Software, which is optional.
 Recommended or required reading: Montgomery, D. C. - Renger, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2003.Karpíšek, Z.: Matematika IV. Pravděpodobnost a statistika. Učební text FSI VUT v Brně. Akademické nakladatelství CERM: Brno, 2003.Hahn, G. J. - Shapiro, S. S.: Statistical Models in Engineering.New York : John Wiley & Sons, 1994.Karpíšek, Z., Drdla, M.: Applied Statistics. Textbook. Brno : FME BUT, 2007. File ApplStat2007.pdf . Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : Plus, 1994.Anděl, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005.
 Planned learning activities and teaching methods: The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
 Assesment methods and criteria linked to learning outcomes: Course-unit credit requirements: active participation in seminars, mastering the subject matter, the total number of points both written exams and semester assignment at least 12 points. Examination (written form) 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, linear regression model) using the summary of formula; a theoretical part (5 tasks related to basic notions, their properties, sense and practical use); evaluation: each task 0 to 15 points and each theoretical question 0 to 3 points; evaluation according to the total number of from examination and seminars: 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).
 Language of instruction: Czech
 Work placements: Not applicable.
 Course curriculum: Not applicable.
 Aims: The course objective is to make students acquainted with basic notions, methods and progresses of probability theory, descriptive statistics and mathematical statistics as well as with the development of students` stochastic way of thinking for modelling a real phenomenon and processes in engineering branches.
 Specification of controlled education, way of implementation and compensation for absences: Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Type of course unit:

Lecture: 26 hours, optionally Ing. Josef Bednář, Ph.D.doc. RNDr. Zdeněk Karpíšek, CSc.doc. RNDr. Libor Žák, Ph.D. 1. Random events and their probability. 2. Conditioned probability, independent events. 3. Random variable, types, functional characteristics. 4. Numerical characteristics of random variables. 5. Basic discrete distributions Bi, H, Po (properties and use). 6. Basic continuous distributions R, N (properties and use). 7. Two-dimensional discrete random vector, types, functional and numerical characteristics. 8. Random sample, sample characteristics (properties, sample from N). 9. Parameters estimation (point and interval estimates of parameters N and Bi). 10. Testing statistical hypotheses (types, basic notions, test). 11. Testing hypotheses of parameters of N, Bi, and tests of fit. 12. Elements of regression analysis. 13. Linear model, estimations and testing hypotheses. 26 hours, compulsory Ing. Pavel HrabecIng. Tomáš Kisela, Ph.D.Ing. Lukáš KokrdaIng. Jakub KůdelaIng. Karel Martišek, Ph.D.RNDr. Karel Mikulášek, Ph.D.Mgr. Aleš Návrat, Ph.D.RNDr. Pavel Popela, Ph.D. 1. Descriptive statistics (one-dimensional sample with a quantitative variable). 2. Descriptive statistics (two-dimensional sample with a quantitative variables). Combinatorics. 3. Probability (calculating by means m/n and properties). Semester work assignment. 4. Conditioned probability. Independent events. 5. Written exam (3 tasks, maximum 10 points). Functional and numerical characteristics of random variable. 6. Functional and numerical characteristics of random variable - achievement. 7. Probability distributions (Bi, H, Po, N).8. Two-dimensional discrete random vector, functional and numerical characteristics. 9. Written exam (3 examples, maximum 10 points). 10. Point and interval estimates of parameters N and Bi. 11. Testing hypotheses of parameters N and Bi. 12. Testing hypotheses of parameters N and Bi - achievement. Tests of fit. 13. Linear regression (straight line), estimates, tests and plot. Assignment evaluation (maximum 5 points).

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