Mathematics 6B

The course is not on the list Without time-table

Code	Completion	Credits	Range
01M6B	Z,ZK	5	2+2s

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Ordered sample, ordered statistics. Point estimates of parameters. Maximum likelihord method. Interval of reliability. Hypotheses testing. Goodness-of-fit test. Correlation and regression. Stochastic processes. Reliability. Reliability of systems. Reliability of renewable systems. Approximation of functions. Numerical integration. Least squares. Fourier series. Orthogonal systems.

Requirements:

Syllabus of lectures:

1. Fundamentals of measure theory, (Lebesgue-Stieltjes) integral and

probability.

2. Radon-Nikodym theorem and its applications in probability.

3. Limit theorems in probability.

4. Random sample, statistics and their distributions.

5. Statistical estimation: basic notions and Cramér-Rao inequality.

6. Point estimation: moment and maximum likehood methods.

7. Interval estimation and statistical hypothesis tests.

8. Multinomial distribution and chi-square test of goodness of fit.

9. The method of least squares, regression and correlation.

10. Stochastic processes.

11. Markov processes with discrete time and states.

12. Classification of the states of a Markov chain.

13. Invariant distribution of a Markov chain.

14. Reserve.

Syllabus of tutorials:

1. Fundamentals of measure theory, (Lebesgue-Stieltjes) integral and

probability.

2. Radon-Nikodym theorem and its applications in probability.

3. Limit theorems in probability.

4. Random sample, statistics and their distributions.

5. Statistical estimation: basic notions and Cramér-Rao inequality.

6. Point estimation: moment and maximum likehood methods.

7. Interval estimation and statistical hypothesis tests.

8. Multinomial distribution and chi-square test of goodness of fit.

9. The method of least squares, regression and correlation.

10. Stochastic processes.

11. Markov processes with discrete time and states.

12. Classification of the states of a Markov chain.

13. Invariant distribution of a Markov chain.

14. Reserve.

Study Objective:

Study materials:

[1] M. K. Ochi: Applied Probability & Stochastic Processes in Engineering. Wiley 1989.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

Ekonomika a řízení elektrotechniky a energetiky-inženýrský blok (compulsory course)
Ekonomika a řízení elektrotechniky a energetiky-inženýrský blok (compulsory course)