Random Variables and Random Vectors

Abstract

It often happens that we do not really care about the outcome of an experiment itself, but rather we are interested in some consequence of this outcome. For instance, a gambler is not primarily interested in the question whether or not heads comes up, but instead in the financial consequences of such an outcome. Hence the gambler is interested in a function of the outcome, rather than in the outcome itself. Such a function is called a random variable and in this chapter we define and study such random variables.