Let X and Y be two continuous random variables with joint pdf f(x, y) = qx2 y(1 + y)

for 0 x 3 and 0 y 3, and f(x, y) = 0 otherwise.

(a)Find the value of q.

(b) Find the probability P(1 X 2, 0 Y 1).

(c) Determine the joint cdf of X and Y for a and b between 0 and 3.

(d) Find marginal cdf FX(a) for a between 0 and 1.

(e) Find the marginal pdf fX(x) directly from f(x, y) and check that it is the derivative of FX(x)

(f) Are X and Y independent?