ABSTRACT
Expectation is a probabilistic interpretation and generalization of the notion of weighted average. For example, suppose that we repeatedly toss a pair of distinguishable fair coins. If X denotes the total number of heads that come up on each toss, then, in the long run, X takes on the values 0, 1, and 2 with relative frequencies .25, .5, and .25, respectively. The average value of X, that is, the average number of heads in the long run, is therefore (.25)0 + (.5)1 + (.25)2 = 1. This idea may be made precise for a general random variable X. For our purposes, however, it is sufficient to consider two special cases: discrete and continuous random variables.
