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Math Help - expected value of conditional density funtion (urgent)

  1. #1
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    expected value of conditional density funtion (urgent)

    the joint density of X and Y is given by
    f(x,y)= (e^-(x/y)*e^-y)/y 0 <x < inf , 0 < y < inf

    show E(x]y=y)

    so i worked out the conditional density function=
    (e^-x/y )/y (confirmed to be correct)
    now i need to integrate from 0 to infinity integral [x*(e^-x/y )/y dx] right???

    i'm trying to integrate by parts
    I cant show this to = y
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  2. #2
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    Quote Originally Posted by mtlchris View Post
    the joint density of X and Y is given by
    f(x,y)= (e^-(x/y)*e^-y)/y 0 <x < inf , 0 < y < inf

    show E(x]y=y)

    so i worked out the conditional density function=
    (e^-x/y )/y (confirmed to be correct)
    now i need to integrate from 0 to infinity integral [x*(e^-x/y )/y dx] right???

    i'm trying to integrate by parts
    I cant show this to = y
    Please show all your working and say where you get stuck.

    Note: Wolfram|Alpha

    Be sure to click on Show Steps.

    To do the definite integral, which is an improper integral, you need to set up a limit.
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