84. You are driving on a highway at speed X1. Cars entering this highway after you travel at speeds X2, X3, . . . . Suppose these Xi s are independent and identically distributed with pdf f (x) and cdf F(x).

Unfortunately there is no way for a faster car to pass a slower one it will catch up to the slower one and then travel at the same speed. For example, if X1 

52.3, X2  37.5, and X3  42.8, then no car will catch up to yours, but the third car will catch up to the second. Let N  the number of cars that ultimately travel at your speed (in your cohort ), including your own car. Possible values of N are 1, 2, 3, . . . . Showthat the pmf of N is p(n)1/[n(n 1)], and then determine the expected number of cars in your cohort. Hint: N  3 requires that X1  X2, X1  X3, X4  X1.