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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 = Xoccurs 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 N/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 P(x). Hence, the quantity XN./N tends to xP(x). Thus, we can tert De Random Variation Pretty 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 meant 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: P(0) = 0.81 P(1) = 0.17 P(2) = 0.02