Given the following table that arranges the data of Alex Rodriguez hits in his 2007 MVP season for the New York Yankees, in terms of the number of bases for a hit, counting 0 bases for the times when he did not get a hit and 4 bases for home runs.
Number of Bases (x): 0 1 2 3 4
Number of Times f(x): 400 98 31 0 54
Recall that the expected value of an event is given by the sum of the products of x and f(x).
Thus, E(x) = ∑xf(x) = 0(400) + 1(98) + 2(31) + 3(0) + 4(54) = 98 + 62 + 216 = 376.
Given that he made a total of 583 at bats, E(x) can be expressed as 376 / 583 = 0.645 to the nearest thousandth.
Therefore, E(X), the expected number of bases for Alex Rodriguez in a typical at bat in 2007 is 0.645