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Math Help - conditional

  1. #1
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    conditional

    given that f(x,y) = exp (-(x+y)) for x>0 and y>0,

    for any y>0, what is the conditional density function of X given that Y=y?

    my working:

    from how i see it, its the
    marginal density of X divided by the the marginal density of X = 1

    what is wrong with my reasoning? help is greatly appreciated.

    thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    BY inspection the two rvs are indep.

    so f(x|y)=f(x)=e^{-x} where x>0
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