Random Variables and Probability Distributions

Abstract

In Chap. 2, we introduced the concept of probability and explored some of the basic properties of probability. In particular, we discussed how it pertains to specific simple events or combinations of simple events associated with the sample space of a random process. In most settings, however, we are interested in much more than just these specific events. In fact, it is important that we be able to obtain probabilities for all of the subsets of the sample space for a random process. This leads us to the concept of a random variable to describe the possible outcomes (i.e., sample space) for a random experiment and then naturally to the distribution of the associated probability across the subsets of this sample space (i.e., probability distribution) as described by possible values of the random variable.