Suppose that X and Y are random variables such that (X, Y) must belong to the rectangle in the xy-plane containing all points (x, y) for which 0 ≤ x ≤ 3 and 0 ≤ y ≤ 4. Suppose also that the joint c.d.f. of X and Y at every point (x, y) in this rectangle is specified as follows:
F(x, y) = 1/156 xy(x2 + y).
Determine
(a) Pr(1 ≤ X ≤ 2 and 1 ≤ Y ≤ 2);
(b) Pr(2 ≤ X ≤ 4 and 2 ≤ Y ≤ 4);
(c) The c.d.f. of Y ;
(d) The joint p.d.f. of X and Y;
(e) Pr(Y ≤ X).