For random variables X and Y with finite variance, the law of total variance states that Var(X) =E(Var(X|Y)) + Var(E(X|Y))

For each n, let Var n be the conditional variance analogue of En. Write out a formula that relates two such conditional variances as the formula for the iteration condition relates two conditional expectations. No extra proof is needed for this formula, since it is a consequence of the law of total variance!