Probability Methods in Engineering II
| Code | Completion | Credits | Range |
|---|---|---|---|
| W01A012 | ZK | 60 |
- Lecturer:
- Tutor:
- Supervisor:
- Department of Technical Mathematics
- Synopsis:
-
Identification course with stochastic models, most frequently used in engineering applications. The course is pay to application of markovian processes in reliability and safety stochastic models, modelling of queueing systems, time series analysis.
- Requirements:
-
The basic knowledge of probability theory and mathematical statistics is supposed.
- Syllabus of lectures:
-
1
Random process, characterisation
2
Stationarity, examples of random processes
3
Poisson process
4
Renewal processes, ergodicity
5
Markov process with discrete time
6
Classification of states, stationary distribution
7
Markov process with continuous time
8
Kolmogorov differential equations
9
Queueing models and theirs classification
10
Application to reliability modelling
11
Time series, Box-Jenkins methodology
12
AR. MA , ARMA models
13Decomposition of time series
14
Stochastic simulation
- Syllabus of tutorials:
-
1
Random process, characterisation
2
Stationarity, examples of random processes
3
Poisson process
4
Renewal processes, ergodicity
5
Markov process with discrete time
6
Classification of states, stationary distribution
7
Markov process with continuous time
8
Kolmogorov differential equations
9
Queueing models and theirs classification
10
Application to reliability modelling
11
Time series, Box-Jenkins methodology
12
AR. MA , ARMA models
13Decomposition of time series
14
Stochastic simulation
- Study Objective:
- Study materials:
-
Mukhopadhyay N.: Probability and statistical inference. M. Dekker Inc., 2001.
Ulrich M.: Základy teorie náhodných procesů, ČVUT Praha 1968
Dohnal G.: Teorie hromadné obsluhy, učební texty na http://d.nipax.cz/tho
Basawa I.V., Prakasa Rao B.L.S.: Statistical inference for stochastic processes. Academic Press, 1980
Mukhopadhyay N.: Probability and statistical inference. M. Dekker Inc., 2001.
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans: