Z=(-1/sqrt(n)) * sum from k=1 to n of [1+log(1-Fk)](adsbygoogle = window.adsbygoogle || []).push({});

Fk is a cumulative distribution function which is continious and strictly increasing.

Show that as n->infinity, Z converges to a normal distribution with mean 0 and var 1

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From Taylor series, log(1-x) = -sum from 1 to infinity of (x^n)/n but dont see how this can help at the moment

Ive been looking for anything around the summation of c.d.fs but havent found anything so I think Im unaware of a few theorems which are essential to solving this. Any help appreciated. Been working on this for hours with no success.

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# Homework Help: Proving a normal distribution

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