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Show that if X, Y and Z are random variables then: cov (X, Y ) = E [cov (X, Y | Z)] + cov (E

Show that if X, Y and Z are random variables then:

cov (X, Y ) = E [cov (X, Y | Z)] + cov (E [X | Z], E [Y | Z])

Assume that all conditional expectations and covariances involved are well-defined and finite so that there are no technical issues of this type to worry about.

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