Course detail

Mathematics I

FSI-9MA1Acad. year: 2022/2023

Normal distribution.
Estimation of parameters.
Hypothesis testing.
Analysis of variances.
Tukey's method and Scheffe method.
Linear model.
Coefficient of correlation.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and realize them on PC.

Prerequisites

Rudiments of descriptive statistics, probability theory and mathematical statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through consultations to explanation of basic principles and theories of the discipline.

Assesment methods and criteria linked to learning outcomes

Use of the above-mentioned statistical methods for solving specific problems. Specific problems are selected in agreement with the student. Student's area of study is preferred. The solved, calculated and elaborated tasks serve to evaluate the student.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Students will acquaint with testing statistical hypotheses and with real applications of linear regression methods in technical practice. Formation of a stochastic way of thinking for the creation of mathematical models with an emphasis on engineering disciplines.

Specification of controlled education, way of implementation and compensation for absences

Teaching is a form of consultation.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

F. Egermayer, M. Boháč: Statistika pro techniky, SNTL, Praha 1984 (CS)
J. Anděl: Matematická statistika, SNTL/ALFA, Praha 1978 (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme D-IME-K Doctoral 1 year of study, winter semester, recommended course
  • Programme D-IME-P Doctoral 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

1. Collection of data.
2. Variance.
3. Pareto analysis.
4. Probability density and probability distribution.
5. Normal distribution.
6. Distribution of averages
7. Estimation of parameters.
8. Hypothesis testing.
9. Analysis of variances. One way testing,
10. Two way testing.
11. Tukey's method. Scheffe method.
12. Linear model.
13. Coefficient of correlation. Partial coefficient of correlation.
14. Statistics modelling. Monte Carlo method.