# how to transform??

• Nov 18th 2008, 07:15 PM
solskjaer
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
• Nov 18th 2008, 11:51 PM
mr fantastic
Quote:

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 $Y = U - UV$.
• Nov 19th 2008, 12:35 AM
solskjaer
thanks, but i hv another question, can we creat whatever ghost variable we want??
• Nov 19th 2008, 01:44 AM
mr fantastic
Quote:

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.