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Probability distribution without a mean?

  1. Feb 13, 2007 #1
    I don't see how this is possible? how can you have a distrubution with no mean?
    My professor says there is, but i don't get it...
  2. jcsd
  3. Feb 13, 2007 #2

    matt grime

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    Exercise: find a series


    that has a finite sum (and hence is can be made to have sum 1, and be a prob distribution on N) but where a_1+2a_2+3a_3+... is not finite (so there isn't a mean).

    And there are less contrived examples too.
  4. Feb 13, 2007 #3


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    Simple example a_k=1/k^2
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