Register to reply

Central limit theorem

Share this thread:
PineApple2
#1
May3-12, 03:16 AM
P: 34
Hello. This is the most closely matching forum I found for this, so I hope my question fits here. I was looking at the following proof of the Central-Limit theorem:
http://physics.ucsc.edu/~peter/250/deriv_climit.pdf
and after Eq. (10) it says: "Expanding out the exponential in the last expression and comparing
powers of k one finds that the fi rst few cumulants are..."
but I don't see how the equalities in the next lines stem from it.
Could someone please explicitly show that?

Thanks.
Phys.Org News Partner Science news on Phys.org
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home
chiro
#2
May3-12, 04:06 AM
P: 4,572
Quote Quote by PineApple2 View Post
Hello. This is the most closely matching forum I found for this, so I hope my question fits here. I was looking at the following proof of the Central-Limit theorem:
http://physics.ucsc.edu/~peter/250/deriv_climit.pdf
and after Eq. (10) it says: "Expanding out the exponential in the last expression and comparing
powers of k one finds that the fi rst few cumulants are..."
but I don't see how the equalities in the next lines stem from it.
Could someone please explicitly show that?

Thanks.
Hey PineApple2.

I think the best way for you would be to look at how the moments and cumulants are defined with respect to each other:

http://en.wikipedia.org/wiki/Cumulant
http://en.wikipedia.org/wiki/Moment_%28mathematics%29

Specifically with regard to your question:

http://en.wikipedia.org/wiki/Cumulan...ts_and_moments


Register to reply

Related Discussions
Central Limit Theorem Calculus & Beyond Homework 2
Central Limit Theorem Precalculus Mathematics Homework 2
Central Limit Theorem Calculus & Beyond Homework 0
Central limit theorem Calculus & Beyond Homework 2
Central limit theorem Calculus & Beyond Homework 4