A privately owned liquor store operates both a drive-in 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-in and walk-in facilities are in use, and suppose that the joint density function of these random variables is given by
f(x,y) = { 2/3(x + 2y), 0 <= x <= 1, 0 <= y <= 1
0, elsewhere.
Find the marginal density of X with proper support.
Find the marginal density of Y with proper support.