Law of Total Variance - Higher Moments

Higher Moments

A similar law for the third central moment μ₃ says

$\mu_3(Y)=\operatorname{E}(\mu_3(Y\mid X))+\mu_3(\operatorname{E}(Y\mid X)) +3\,\operatorname{cov}(\operatorname{E}(Y\mid X),\operatorname{var}(Y\mid X)).\,$

For higher cumulants, a simple and elegant generalization exists. See law of total cumulance.

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