Suppose that X,Y and X,Z are bivariate normally distributed. We have
$E(X)=0, Var(X)=10$, $E(Y)=0, Var(Y)=6$ and $ρ_{xy}=0.87$
Moreover,
$E(X)=0, Var(X)=10$, $E(Z)=0, Var(Z)=4$ and $ρ_{xz}=0.87$
Indicating as K the joint distribution of Y and Z,i know from the theory of the problem i'm dealing with that K is for sure a bivariate normally distributed. I expect this will pose some constraint on the value of $ρ_{yz}$
Posted also here: https://stats.stackexchange.com/questions/414312/correlation-coefficient-bivariate-normally-distributed