申論題

4. A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X = the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y = the proportion of time that the walk-up window is in use. Then the set of possible values for (X, Y) is the rectangle D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}. Suppose the joint probability density function (pdf) of (X, Y) is given by

(b) The marginal pdf of X, which gives the probability distribution of busy time for the drive-up facility
without reference to the walk-up window, is__(F)__.