Functions of Random Variables

Milan Holický
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Milan Holický: Czech Technical University in Prague, Klokner Institute, Department of Structural Reliability

Chapter Chapter 7 in Introduction to Probability and Statistics for Engineers, 2013, pp 79-93 from Springer

Abstract: Abstract Functions of random variables defining resulting random variables as functions of several input random variables regularly enter many engineering and scientific applications. The elementary functions of a single continuous variable and two or more independent variables, reviewed in Appendix 4, are supplemented by functions several random variables. A special function of a single random variable is the extreme value of samples taken from a population described by various types of so-called extreme value distributions. These distributions play a substantial role in a number of practical applications. Another important function of a random variable is the updating of its probability distribution when newly obtained information is taken into account. This procedure is developed as an extension of Bayes´ theorem. Finally, the distribution of a sum of several random variables is discussed in conjunction with the central limit theorem.

Keywords: Central Limit Theorem; Moment-based Parameter; Classical Extreme Value Theory; Parent Distribution; Prior Probability Density Function (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-38300-7_7

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