I'm working on a book about normal copula function. The book provides a graph of the pdf of bivariate normal and it seems that when correlation is increasing, the cdf of bivariate is incresing because the pdf will become larger in lower left corner. However, although it seems straight forward, I just failed to prove it.
So, I'm wondering is the of CDF of standard bivariate normal is increasing in ρ (the correlation parameter)? If so , how to prove it?
Thank you!