I have the following question I need to answer.

SupposeX1 andX2 are two standard normals and are joint normal with correlationρ. Compute the Gaussian copula functionC(u1,u2) for (X1,X2) with the following value ofρ

ρ= 0

ρ= 1

ρ= 0.5 (In this case, the copula function has no closed form inu1 andu2. So just write down the simplest expression you can derive.)

- Express the copula for (
X1,X3) in terms of the copula function in part (c)

As far as I can tell, C is the cdf of a bivariate normal distribution, but I'm not sure what to do when the correlation is 1, since it is undefined then and it should be the minimum of the marginals. Also, I'm not sure how to start section d. I would greatly appreciate any help. Thanks!