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Math Help - proof of expectation with CDF

  1. #1
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    proof of expectation with CDF

    Hey guys! I need help in completing the proof.
    The proof starts like this
    E[X]=E[X^+]-E[X^-]=\int_{0}^{\infty} xdF_x^+(x)\, dx - \int_{0}^{\infty} xdF_x^-(x)\,dx
     = \int_{-\infty}^{\infty} xdF_x(x)\, dx<br />


    I cant find the reason for the last line. Please give me a clue.
    Last edited by adhd; March 15th 2009 at 04:20 AM. Reason: Latex syntax error
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  2. #2
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    Remember that:

    \int_a^b f(x)dx=-\int_b^a f(x)dx, and try to work from there using the properties of the propability function
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  3. #3
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    ^Thank you for the clue!
    Last edited by adhd; March 16th 2009 at 05:50 AM. Reason: error in grammar
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