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Math Help - integration in probability

  1. #1
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    integration in probability

    how to integrate x(1/sqrt(2pi))(exp(-(x-y)^2/2)) with respect to x from infinity to infinity? the answer is y. but how do you get that?
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  2. #2
    MHF Contributor matheagle's Avatar
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    This integral is the mean of X. When X\sim N(Y,1).

    You can let Z=X-Y\sim N(0,1).

    There are many ways to show that \int_{\infty}^{\infty}z e^{-z^2/2}dz=0.

    The easiest way is to note that the integrand is an odd function.
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