Let (X, Y ) be a couple of continuous random variables with joint density

f(X,Y )(x, y) = (x ^2 + y^ 2 ) for x [1, 2] and y [1, 2]

0 when (x, y) / [1, 2] [1, 2].

Let A = {X 3 2 and Y 5 4 } and B = {|X Y | 1 4 }.

1. Compute .

2. Compute P(A).

3. Compute P(B). Hint: draw the integration region and split the integral in three parts.

4. Are X and Y independent random variables? Justify