Question: For all random variables X, Y, and Z, let Cov(X, Y |z) denote the covariance ofX and Y in their conditional joint distribution given Z

For all random variables X, Y, and Z, let Cov(X, Y |z) denote the covariance ofX and Y in their conditional joint distribution given Z = z. Prove that
Cov(X, Y) = E[Cov(X, Y |Z)]
+ Cov[E(X|Z), E(Y|Z)].

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