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 propor- tions 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)= 32 (x+2y), for 0≤x≤10≤x≤1, 0≤y≤1,0≤y≤1,$$ f(x, y)=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.