Question: Suppose that the waiting time for a bus, in minutes, has the uniform in (0, 10) distribution. In five months a person catches the bus 120 times. Find an approximation to the 95th percentile of the person's total waiting time. (Hint. The mean and variance of a uniform(0, 10) distribution are 5 and 100/12, respectively; see Examples I and II.)
Example I: Let Y ∼ U(A, B), that is, Y has the uniform in [A, B] distribution (see Example 3.2-5). Show that E(Y) = (B + A)/2.
Examples II: Let X ∼ U(0, 1), that is, X has the uniform in [0, 1] distribution (see Example 3.2-4). Show Var(X) = 1/12.