Random Variables

Abstract

The standard situation in the modeling of a random phenomenon is that the quantities of interest, rather than being defined on the underlying probability space, are functions from the probability space to some other (measurable) space. These functions are called random variables. Strictly speaking, one uses the term random variable when they are functions from the probability space to $$\mathbb R $$ . If the image is in $$\mathbb R ^n$$ for some $$n\ge 2$$ one talks about $$n$$ -dimensional random variables or simply random vectors. If the image space is a general abstract one, one talks about random elements.