Remark

        •  The above figure illustrates the mapping corresponding to a joint random variable. The joint random variable in the above case is denoted by .

         •  We may represent a joint random variable as a two-dimensional vector .

        •  We can extend the above definition to define joint random variables of any dimension. The mapping such that for is called an n-dimensional random variable and denoted by the vector

      Example1 Suppose we are interested in studying the height and weight of the students in a class. We can define the joint RV where represents height and represents the weight.

      Example 2 Suppose in a communication system is the transmitted signal and is the corresponding noisy received signal. Then is a joint random variable.