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The law of total variance,
a.k.a. variance decomposition formula,
a.k.a. conditional variance formulas,
a.k.a. the law of iterated variances,
a.k.a. Eve's law
Var(Y) = E(Var(Y|X)) + Var(E(Y|X))
The law of total covariance,
a.k.a. the covariance decomposition formula,
a.k.a. the conditional covariance formula
Cov(Y,Z) = E[Cov(Y,Z|X)] + Cov[E(Y|X), E(Z|X)]
#stats #math