ABSTRACT
Once a random variable has been dened, there can be many reasons for dening functions of that variable. One reasonable example would be a conversion of a temperature measurement from a Celsius scale to a Fahrenheit scale. Another would be the conversion from sales volume to revenue. In general, since a random variable is a function for which the range is the real line, the construction of another function-a function of the random variable-should be a reasonable thing to do and should conform to usual algebraic behaviors. The corresponding distribution function for the functional variable can be constructed at the same time. This is an important extension of the probability concepts treated in this text, so it is included in this chapter. However, the analysis of general functions of random variables and random vectors is placed later in the chapter because there is a particular function-called expectation-that is central to many probability analyses.
