Show that:

$\displaystyle P(a_1 < X < a_2, b_1 < Y < b_2) = F(a_2, b_2) + F(a_1, b_1) - F(a_1, b_2) - F(a_2, b_1)$

I started with:

$\displaystyle P (a_1 < X < a_2, b_1 < Y < b_2) = P (a_1 < X < a_2 \cap b_1 < Y < b_2)$

$\displaystyle = P (a_1 < X < a_2) \cap (b_1 < Y < b_2)$

$\displaystyle = P (a_1 < X < a_2) + (b_1 < Y < b_2) - P (a_1 < X < a_2) \cup (b_1 < Y < b_2)$

but then i get stuck

Also I just to check: $\displaystyle P(X < a, Y < b)= P(X<a) \cap P(Y<b)$