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Mean of a Distribution Question

  1. Feb 7, 2010 #1
    Here goes:

    If F is a probability distribution function and /phi is its integrable characteristic function. If the mean of F exists, why can we say that there exists u>0 st int[abs(1- /phi(t))/t] < infinity, where the integral is over the set of all t st abs(t)<u ?

    (abs = absolute value)

    I just. Can`t. See. It.

    Thanks in advance for your help.
     
  2. jcsd
  3. Feb 7, 2010 #2

    mathman

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    Science Advisor
    Gold Member

    I'm not completely sure of details, but you would use phi(t) ~ 1 +iFt for t near 0.
     
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