I want to find the Value of joint CDF at $x=-\infty, y=+\infty, F_{XY}(-\infty,+\infty)$
My attempt
$F_{XY}(-\infty,+\infty) = \int_{x=-\infty}^{-\infty}\int_{y=-\infty}^{+\infty}f_{XY}(x,y) dydx \\ = \int_{x=-\infty}^{-\infty} f_X(x) dx \\ = 0$
But in classnotes, it is answer is given as 1. I am not able to find where i went wrong. Kindly correct me.
$F(x,y)=P(X\le x, Y\le y)$. Hence, $F(\infty,\infty)=P(X< \infty,Y<\infty)=1$
On the other hand,
$F(-\infty,\infty)=P(X< -\infty,Y<\infty)=0$