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Thread: proof of expectation with CDF

  1. March 15th 2009, 04:08 AM #1
    adhd
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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. March 15th 2009, 11:21 PM #2
    djadooghar
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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. March 16th 2009, 05:48 AM #3
    adhd
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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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