I have the following question I need to answer.

Suppose X1 and X2 are two standard normals and are joint normal with correlation ρ. Compute the Gaussian copula function C(u1, u2) for (X1, X2) with the following value of ρ

  1. ρ = 0
  2. ρ = 1
  3. ρ = 0.5 (In this case, the copula function has no closed form in u1 and u2. So just write down the simplest expression you can derive.)
  4. 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. Would it just be C(u1,(u2)^(1/3))? I would greatly appreciate any help. Thanks!