Gekko

08-23-2010, 09:42 PM

Hi, I've been struggling with the below and have no idea how to tackle it. I've looked at the mgf but this doesn't seem to work out.

Intuitively I imagine if we can obtain the mgf of the normal then the proof is complete? Ie exp(t^2/2) for mean 0 and var 1

Any help greatly appreciated. Stumped!!

Z=(-1/sqrt(n)) * sum from k=1 to n of [1+log(1-Fk(Xk))]

where Fk is a cumulative distribution function which is continious and strictly increasing. Xk is independent random variable

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

Intuitively I imagine if we can obtain the mgf of the normal then the proof is complete? Ie exp(t^2/2) for mean 0 and var 1

Any help greatly appreciated. Stumped!!

Z=(-1/sqrt(n)) * sum from k=1 to n of [1+log(1-Fk(Xk))]

where Fk is a cumulative distribution function which is continious and strictly increasing. Xk is independent random variable

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