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Example where higher moments are infinite

  1. Oct 25, 2009 #1
    Can someone give me an example where we have [tex]\mathbb{E}z=0 [/tex], [tex]\mathbb{E}z^2=1 [/tex] (i.e. finite expectations)
    BUT,
    [tex]\mathbb{E}z^4= \infty [/tex] ?

    Also, I cannot think of a case where:
    [tex]\mathbb{E}x=\infty [/tex] where [tex]x>0[/tex]
    BUT,
    [tex]\mathbb{E}| \log x |< \infty [/tex]

    Thanks in advance
     
  2. jcsd
  3. Oct 25, 2009 #2

    mathman

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    For your first question, let the density function f(x)=k/(1+x4).

    For the second, f(x)=c/(1+x2) for x>0, f(x)=0 for x<0.
     
  4. Oct 26, 2009 #3
    Try the Pareto distribution.
     
  5. Oct 26, 2009 #4
    Thank you very much. It makes sense
     
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