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Proof of expected value expression

  1. Oct 3, 2005 #1
    The usual expression of the expected value of X is:
    E[X] = (sum) x*p(x)

    i'm supposed to show that, for X a random non-negative discrete random(stochastic) variable, we have that:
    E[X]=(sum: i from 1 to infinity) P(X>=i)

    i have absolutely no idea how to do this. does anyone want to push me in the right direction?
  2. jcsd
  3. Oct 3, 2005 #2


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    Science Advisor

    P(X>=i)=sum(j=i,inf) P(X=j). Plug this into your sum over i, interchange i and j and you will get what you want, since the sum over i will simply be j.
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