# Math Help - how to transform??

1. ## 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

2. Originally Posted by solskjaer
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 $Y = U - UV$.

3. thanks, but i hv another question, can we creat whatever ghost variable we want??

4. Originally Posted by solskjaer
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.