The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x < y, and assume that the joint density function of these variables is
(a) Determine if X and Y are independent.
(b) Find P (l/4 < X < 1/2 | Y = 3/4).