If the joint probability distribution of X and Y is given by:
A privately owned liquor store operates both drive-in facility and walk-in facility. On randomly selected day, let X and Y, respectively, be the proportions of time that the drive-in and walk-in facilities are in employ, and assume that the joint density function of these random variables is
f(x, y) = (2/3)(x + 2y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
0, elsewhere.
a) Find out the marginal density of X.
b) Find out the marginal density of Y.
c) Find out the probability that the drive-in facility is busy less than one-half of the time.