Course detail

Mathematics I

FSI-9MA1Acad. year: 2024/2025

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)

Entry knowledge

Rudiments of descriptive statistics, probability theory and mathematical statistics.

Rules for evaluation and completion of the course

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.

Teaching is a form of consultation.

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.

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.

Study aids

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