=+34.17. 1 Application of mixing to the central limit theorem. Let X , X ;,... be random variables on (2, 9, P), independent and identically distributed with mean 0 and variance o2, and put S ,, = X, + . .. + X ,,. Then S/o = N by the Lindeberg-Levy theorem. Show by the steps below that this still holds if P is replaced by any probability measure Po, on (2, 9 ) that P dominates. For example, the central limit theorem applies to the sums E"_ " (w) of Rademacher functions if w is chosen according to the uniform density over the unit interval, and this result shows that the same is true if w is chosen according to an arbitrary density.