Random Variables

It has been stressed in the foregoing chapters that the probability of a random event can be discussed only with reference to a sample description space on which a probability function has been defined. However, in many applications of probability theory the terminology of sample description spaces does not explicitly enter (although, as we shall see, the notion is always implicitly present). Rather, many applications of probability theory are based on the notion of a random variable . This chapter gives a rigorous definition of the notion of a random variable and presents the main concepts and techniques used to treat random variables.