# Random phenomena

Random phenomena is a 2nd semester elective general course held at University of Ljubljana, Slovenia.

### Semester

2. semester - University of Ljubljana, Slovenia

### Lecturer

prof. dr. Edvard Govekar

### Course Points (ECTS)

5.0

### Contact Information

University of Ljubljana, Slovenia

## Course Overview

### Module objective

- to introduce the concepts of variability, description, characterisation and interpretation of random data
- to acquaint the students with the concept of probability and the basic statistical methods for the description and characterisation of random data
- to equip the students with the basic knowledge for the analysis, description, characterisation and interpretation of experimental data
- using the Matlab environment
- the ability to analyse, characterise and interpret variable random data
- the ability to conduct linear analysis and characterise sensor signals using the methods of technical statistics for the description, analysis, characterisation, design and planning of products, technical systems and processes

### Knowledge outcome

The students obtain the knowledge about:

- the fundamentals of probability and statistical description of random phenomena,
- the fundamentals of time series/sensor signal analysis using the statistical methods of description, deduction and interpretation of data variability in the characterisation and design of products, systems and processes.

The students will understand:

- the concepts of variability, randomness, probability, probability distribution of random variables,
- the assumptions and principles of statistical analysis and deduction,
- the assumptions of stationariness and the ergodicity principles in the analysis of random processes.

### Syllabus outline

- Introduction: examples of random phenomena and the problem of variability in the engineering, experiments and randomness of experiment outcomes, events.
- Probability: relations and event probabilities; random variables and probability distributions, functions of random variables; means and moments ofrandom variables.
- Technical statistics: important statistics, properties and probability distributions of statistics; point estimates; methods for determining estimates; interval estimates; statistical hypotheses, tests and deduction; errors of deduction; goodness-of-fit tests, tests for dependence and homogeneity; analysis of variance; function estimates: parametric and non-parametric regression.
- Random processes: examples of random processes; moments and characteristics; stationariness and ergodicity; linear transforms of random processes, autocorrelation function, spectral density, coherence function, examples of random process characterisation.

### Monitoring of student progress

- written and oral exams
- colloquia
- seminar papers
- credit assessment of individual (verifiable) study achievements

## Literature

[1] I. Grabec, J. Gradišek: Naključni pojavi; Fakulteta za strojništvo, 2000;

[2] E. Govekar; lecture notes; www.nakljucnipojavi.si (2007);

[3] R. Jamnik: Verjetnostni račun in statistika; Zveza organizacij za tehnično kulturo, (1986);

[4] D. C. Montgomery in G. C. Runger: Applied Statistics and Probability for Engineers, John Wiley & Sons, Inc., New York, 1994;

[5] J. S. Bendat, A. G. Piersol: Random Data: Analysis and measurement Procedures; Wiley-Interscience (1971);

[6] W. B. Davenport, Jr.: Probability and Random Processes: An Introduction for Applied Scientists and Engineers, McGraw-Hill, New York, 1970;

[7] R. C. Jaffe: Random signals for engineers usnig Matlab and Mathcad; Spriger Verlag (2000).