Course detail
Mathematics IV
FSI-4MAcad. year: 2022/2023
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Hahn, G. J. - Shapiro, S. S.: Statistical Models in Engineering.New York : John Wiley & Sons, 1994.
Montgomery, D. C. - Renger, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2017.
Recommended reading
Karpíšek, Z.: Matematika IV. Pravděpodobnost a statistika. Učební text FSI VUT v Brně. Akademické nakladatelství CERM: Brno, 2003.
Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : Plus, 1994.
Elearning
Classification of course in study plans
- Programme B-FIN-P Bachelor's 2 year of study, summer semester, compulsory
- Programme B-MET-P Bachelor's 2 year of study, summer semester, compulsory
- Programme B-ZSI-P Bachelor's
specialization STI , 2 year of study, summer semester, compulsory
specialization MTI , 2 year of study, summer semester, compulsory - Programme N-PMO-P Master's 1 year of study, summer semester, compulsory-optional
- Programme LLE Lifelong learning
branch CZV , 1 year of study, summer semester, compulsory-optional
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.
Exercise
Teacher / Lecturer
Syllabus
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).
Computer-assisted exercise
Teacher / Lecturer
Syllabus
2. Descriptive statistics
3. Probability distributions (Bi, H, Po, N).
4. Point and interval estimates of parameters N and Bi.
5. Testing hypotheses of parameters N and Bi. Tests of fit.
6. Linear regression (straight line), estimates, tests and plot.
Elearning