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 $\displaystyle U = \frac{X}{X+Y}$ 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 $\displaystyle Y = U - UV$.