Random Variables

          In application of probabilities, we are often concerned with numerical values which are random in nature. For example, we may consider the number of customers arriving at a service station at a particular interval of time or the transmission time of a message in a communication system. These random quantities may be considered as real-valued function on the sample space. Such a real-valued function is called real random variable and plays an important role in describing random data. We shall introduce the concept of random variables in the following sections.

   Mathematical Preliminaries

  Real-valued point function on a set

          Recall that a real-valued function  maps each element , a unique element .The set is called the domain of and the set is called the range of . Clearly . The range and domain of are shown in Figure 1.