[R] bivariate normal and rho

[Agostino Capponi]

Hi,

Let f(rho) = E[F_1(x) F_2(y)], i.e f(rho) is the expectation of
F(x) * F(y) with respect to the bivariate Gaussian density with mean 0
and covariance matrix [1 rho; rho 1].
Moreover, assume F_1(x) and F_2(y) to be increasing functions of x and y
respectively.

I was wondering if it was true that f(rho) is an increasing function of rho.
If so, are there any references?

Best,

Agos