Multiple Random Variables

           In many applications we have to deal with more than two random variables. For example, in the navigation problem, the position of a space craft is represented by three random variables denoting the x, y and z coordinates. The noise affecting the R, G, B channels of colour video may be represented by three random variables. In such situations, it is convenient to define the vector-valued random variables where each component of the vector is a random variable.

           In this lecture, we extend the concepts of joint random variables to the case of multiple random variables. A generalized analysis will be presented for random variables defined on the same sample space.

    Joint CDF of random variables

           Consider random variables defined on the same probability space We define the random vector X as,