# correlation coefficient bivariate normally distributed [duplicate]

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 $$ρ_{xz}=0.87$$

Will also Y and Z be bivariate normally distributed ? (I guess yes) If yes, which is their coefficient of correlation?

Added after comment of Whuber: 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 $$ρ_{yz}$$

## marked as duplicate by Glen_b♦Jun 23 at 23:14

• Comment after some thought on the problem i'm dealing with. 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 $ρ_{yz}$ – Andrea Mazzolari Jun 23 at 14:55