Thread: 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

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 and 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: and .

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

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.