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A question on multi-Gaussian

  1. Oct 17, 2009 #1
    Could anyone help me evaluate the integral
    [itex]
    \intop_{-\infty}^{\infty}\intop_{-\infty}^{\infty}|sx+ty|e^{-s^{2}/2}e^{-t^{2}/2}dsdt
    [/itex], which should be a function of x and y?

    By the way, this is not a homework problem.

    Thanks
     
  2. jcsd
  3. Oct 17, 2009 #2

    mathman

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    Science Advisor
    Gold Member

    You will have to divide the domain of integration into two parts along the line sx+ty=0 (for fixed x and y) and integrate separately. I believe the result will involve erf (integral of Gaussian).
     
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