Q1) If joint probability distribution of X and Y is given by:

Privately owned liquor store operates both drive-in facility and walk-in facility. On randomly selected day, let X and Y, respectively, be proportions of time that the drive-in and walk-in facilities are in use, and assume that joint density function of these random variables is

f(x, y) =    (2/3)(x + 2y),           0 ≤ x ≤ 1, 0 ≤ y ≤ 1,

0, elsewhere.

i) Determine the marginal density of X.

ii) Determine the marginal density of Y.  

iii) Determine the probability that drive-in facility is busy less than one-half of the time.