MathGroup Archive 2012

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Moment function

  • To: mathgroup at
  • Subject: [mg126952] Moment function
  • From: paul <paulvonhippel at>
  • Date: Wed, 20 Jun 2012 03:48:55 -0400 (EDT)
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I would like a formula for the mth moment of Z^p, where Z~Normal(mu,sigma) and p is a positive integer. With m=p=1, the answer should be mu -- i.e., the first moment of a normal variable is the mean mu. But that's not what I get when I do it this way:

momentPN = 
    Z \[Distributed] NormalDistribution[\[Mu], \[Sigma]]], m], {m > 0,
    p > 0, Element[p, Integers], Element[m, Integers]}]

 momentPN /. {p -> 1, m -> 1}, {\[Sigma] > 0, Element[\[Mu], Reals]}]

I know other ways to get the right answer, but why doesn't this method work?

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