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where the notation indicates that the summation extends over all possible val- ues of x. The expected value of a random variable is also called its mean and is denoted We can express expected value in terms of long-run relative frequencies. Suppose that a random experiment is repeated N times and that the event "X = x" occurs in N, of these trials. The average of the values taken by the random variable over all N trials will then be the sum of XN,/N over all possible values of x. Now, as the number of replications, N, becomes infinitely large, the ratio N./N tends to the probability of the occurrence of the event "X = x" that is, to PC.x). Hence, the quantity N./N tends to xP(x). Thus, we can Chapter 4 Discrete Random Variables and Probability Distributions 28 view the expected value as the long run average value that a random variable takes over a large number of trials. Recall that in Chapter 2 we used the mean for the average of a set of numerical observations. We use the same term for the expectation of a random variable Example 4.3 Errors in Textbooks (Expected Value) Suppose that the probability distribution for the number of errors, X. on pages from business textbooks is as follows: PO 1 SL PI 0.17 P2 01.02 Zoom: Links Desktop Local Disk (D) S Address