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)
    [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]
    [tex]\mathbb{E}| \log x |< \infty [/tex]

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


    User Avatar
    Science Advisor
    Gold Member

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Example where higher moments are infinite
  1. Examples of surjections (Replies: 15)

  2. Higher Cardinals. (Replies: 1)

  3. Higher order moments (Replies: 2)