Let $X$ and $Y$ be standard Gaussian distributed random variables and $\rho(X, Y) = \alpha$. Then what is $P(X > x \cap Y > y)$.
I have attempted some form of integration from $P(X > x \cap Y > y)$ $=$ $P(X > x) \cdot P(Y > y | X > x)$ $=$ $P(X > x) \cdot \frac{f_{X,Y}(x,y)}{f_X(x)}$ to no avail.
Any help would be appreciated as I feel quite stumped, and a cursory literally review did not turn anything up.