Let (X, Y ) be a couple of continuous random variables with joint density f(X,Y )(x, y) = (x 2 + y) for x [0, 1] and y [1, 4]

0 when (x, y) / [0, 1] [1, 4].

Let A = {X 1 2 and Y > 2} and B = {|X Y | > 2}.

1. Compute .

2. Compute P(A).

3. Compute P(B).

4. Are X and Y independent random variables? You need to justify clearly (or give a full proof).