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Central limit theorem

  1. May 3, 2012 #1
    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.
     
  2. jcsd
  3. May 3, 2012 #2

    chiro

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    Science Advisor

    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_(mathematics)

    Specifically with regard to your question:

    http://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments
     
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