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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

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