A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected

Question:

A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is

(r + 2y), (0, 0 <x < 1, 0 < y < 1, elsewhere. f (x, y) =

(a) Find the marginal density of X.
(b) Find the marginal density of Y .
(c) Find the probability that the drive-through facility is busy less than one-half of the time.