Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook