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Homework Help: Finite expectation value <-> finite sum over Probabilties

  1. Nov 23, 2007 #1
    1. The problem statement, all variables and given/known data
    If X is a real valued random variable with E[|X|] finite. <-> [tex]\sum(P(|X|>n))[/tex] finite

    , with the sum over all natural numbers from 1 to infinity.
    2. Relevant equations

    As a tip Im given that for all integer valued X>0 E(X) = [tex]\sum(P(X)>k[/tex] , where the sum goes over all k =1 to k=infinity (k is a natural number)

    3. The attempt at a solution

    I don´t really have an idea i tried to find a way to relate integer valued stuff to real valued stuff by summing over all real valued stuff that are not integer.
    But dont get anywhere :(
    Hope for some advice
  2. jcsd
  3. Nov 23, 2007 #2


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    What is the formula for E[|X|]?
  4. Nov 24, 2007 #3
    It´s just the expectation value E[|X|]= sum over all |x|*P(|x|).
  5. Nov 24, 2007 #4
    ok solved it :)
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