The joint density of X and Y is given by
f(x, y) =⎨xe⁻⁽ˣ⁺ʸ⁾ x > 0, y > 0
0 otherwise

Are X and Y independent? If, instead, f(x, y) were given by
f(x, y) = { 2 < x < y, 0 < y < 1
0 otherwise

would X and Y be independent?