Course detail

# Mathematics IV

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.

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.

Prerequisites

Rudiments of the differential and integral calculus.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Montgomery, D. C. - Renger, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2017.
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.

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.

Classification of course in study plans

• Programme B3A-P Bachelor's

branch B-MTI , 2. year of study, summer semester, 5 credits, compulsory
branch B-MET , 2. year of study, summer semester, 5 credits, compulsory
branch B-FIN , 2. year of study, summer semester, 4 credits, compulsory

• Programme B3S-P Bachelor's

branch B-STI , 2. year of study, summer semester, 5 credits, compulsory
branch B-KSB , 2. year of study, summer semester, 5 credits, compulsory

• Programme M2A-P Master's

branch M-PMO , 1. year of study, summer semester, 4 credits, compulsory-optional

• Programme M2I-P Master's

branch M-LPR , 1. year of study, summer semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

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.

Exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

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).