Course detail

Statistics and Probability

FSI-CS1Acad. year: 2022/2023

The subject is aimed at introduce of students to descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameters estimation, tests of hypotheses, and linear regression analysis. The practices include problems and applications in mechanical engineering. A part of exercises will solving by means of statistical software.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

Ing. Josef Bednář, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Students obtain needed knowledge from the probability theory, descriptive statistics and mathematical statistics, which them will enable understand and apply stochastic models of technical phenomenon and suits, based upon these methods.

Prerequisites

Rudiments of the differential and integral calculus.

Co-requisites

Not applicable.

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

Seminar credit conditions: active attendance in practices, encompassment of complete subject, classification sufficient or better of written exam and admission of semester assignment. Examination (written form): practical part (2 examples from theory of probability: probability and its properties, random variable, distribution Bi, H, Po, N and discrete random vector; 2 examples from mathematical statistics: point and interval estimates of parameters, tests of hypotheses of distribution and parameters, linear regression model) with own summary of formula; theoretical part (4 questions to basic notions, their properties, sense and practical use); evaluation: each example 0 as far as 20 points and every theoretical question 0 as far as 5 points; classification according to of the total sum of points: 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).

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Acquaint of students with basic notions, methods and progresses of probability theory, descriptive statistics and mathematical statistics. Formalization of stochastic way thinking for modeling of real phenomenon and processes in an engineering enclosures.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anděl, J.: Statistické metody. Praha : Matfyzpress, 1993.
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, 2017.
Sprinthall, R. C.: Basic Statistical Analysis. Boston : Allyn and Bacon, 1997.

Recommended reading

Cyhelský, L. - Kahounová, J. - Hindls, R.: Elementární statistická analýza. Praha : Management Press, 1996.
Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
Seger, J. - Hindls, R.: Statistické metody v tržním hospodářství. Praha : Victoria Publishing, 1995.

Classification of course in study plans

  • Programme B-ENE-P Bachelor's 2 year of study, winter semester, compulsory

  • Programme B-STR-P Bachelor's

    specialization AIŘ , 2 year of study, winter semester, compulsory
    specialization KSB , 2 year of study, winter semester, compulsory
    specialization SSZ , 2 year of study, winter semester, compulsory
    specialization STG , 2 year of study, winter semester, compulsory

  • Programme LLE Lifelong learning

    branch CZV , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Mgr. Eva Mrázková, Ph.D.

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.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Josef Bednář, Ph.D.
Ing. Ivan Eryganov, Ph.D.
Ing. Mgr. Eva Mrázková, Ph.D.
doc. RNDr. Libor Žák, Ph.D.
doc. Mgr. Zuzana Hübnerová, Ph.D.
Ing. Matouš Cabalka

Syllabus

1. Introduction to Statistical Software
2. Descriptive statistics
3. Probability
4. Random variable
5. Random vector
6. Probability distributions (Bi, H, Po, N).
7. Point and interval estimates of parameters N and Bi.
8. Testing hypotheses of parameters N and Bi. Tests of fit.
9. Linear regression (straight line), estimates, tests and plot.