Problem 5.63 Let X, Y have the joint pdf f(x, y) = c(x + xy), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, f(x, y)=0,elsewhere.

(a) Compute the value of

c.

(b) Compute the marginal pdfs fX(x) and fY (y).

(c) Are the random variables X and Y independent?

(d) Compute P(X + Y ≤ 1) by first writing it as a double integral of the density f(x, y) over an appropriate region of the plane. Then evaluate the double integral.