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

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- Nov 18th 2008, 06:15 PMsolskjaerhow 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

- Nov 18th 2008, 10:51 PMmr fantastic
You should first consider the random variables $\displaystyle U = \frac{X}{X+Y}$ and $\displaystyle V = X + Y$ 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: $\displaystyle X = UV$ and $\displaystyle Y = U - UV$. - Nov 18th 2008, 11:35 PMsolskjaer
thanks, but i hv another question, can we creat whatever ghost variable we want??

- Nov 19th 2008, 12:44 AMmr fantastic