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Math Help - how to transform??

  1. #1
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    how to transform??

    If X, Y are independent gamma's, find the pdf of X/(X+Y). what i dont understand is why we creat u2= x+y, which is called a ghost variable?? thx
    Last edited by solskjaer; November 18th 2008 at 10:37 PM.
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  2. #2
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    Quote Originally Posted by solskjaer View Post
    If X, Y are independent gamma's, find the pdf of X/(X+Y). what i dont understand is why we creat u2= x+y, which is called a ghost variable?? thx
    You should first consider the random variables U = \frac{X}{X+Y} and V = X + Y and find the joint pdf of U and V (using the transformation theorem). Then use this joint pdf to get the pdf of U.

    The utility of the ghost variable will become clear.

    Note: X = UV and Y = U - UV.
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    thanks, but i hv another question, can we creat whatever ghost variable we want??
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    Quote Originally Posted by solskjaer View Post
    thanks, but i hv another question, can we creat whatever ghost variable we want??
    Yes, but some will lead to easier calculations than others ..... Do the calculation and you'll see.
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