Random phenomena

Random phenomena

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


2. semester - University of Ljubljana, Slovenia


prof. dr. Edvard Govekar

Course Points (ECTS)


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 


[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).