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Math Help - [SOLVED] urgent... i have a question about expectation value.. i need help.

  1. #1
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    [SOLVED] urgent... i have a question about expectation value.. i need help.

    Consider a random variable X that takes only nonnegative integer values. Show that the following
    is a way of computing the expectation of X:
    E(X) = (sum of this function from x=0 to x= infinity) (sum symbol) Pr(X > x)
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  2. #2
    Super Member Anonymous1's Avatar
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    Well, what is P(X>x)?

    It is the cumulative distribution function. What do you get when you sum over the distribution function for all x? What do you get when you sum over the distribution function to some x?
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  3. #3
    Super Member Anonymous1's Avatar
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    I'll just make your life easy.

    \sum_{x=0}^{\infty} P(X>x) = \sum_{j=0}^{\infty}\sum_{x=0}^{j} P(X=j) = \sum_{j=0}^{\infty}jP(X=j) = E[X].

    Note this only necessarily holds for integer-valued non-negative random variates.
    Last edited by mr fantastic; March 27th 2010 at 03:49 PM. Reason: Merged posts
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  4. #4
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    thanks a lot

    it was really important
    Quote Originally Posted by Anonymous1 View Post
    I'll just make your life easy.

    \sum_{x=0}^{\infty} P(X>x) = \sum_{j=0}^{\infty}\sum_{x=0}^{j} P(X=j) = \sum_{j=0}^{\infty}jP(X=j) = E[X].

    Note this only necessarily holds for integer-valued non-negative random variates.
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