Question: 3.40 A fast-food restaurant operates both a drivethrough facility and a walk-in facility. On a randomly selected day, let X and Y , respectively, be

3.40 A fast-food restaurant operates both a drivethrough 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 f(x, y) =

(x + 2y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0, elsewhere.

(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.

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