Use the change-of-variable technique to find the joint distribution of Y1, Y2, and Y3. It shouldn't really be necessary to determine the distributions of the individual Y's.
I have a problem about an exercise :
We consider 3 random variables X1 X2 X3 , exponentially distributed with mean =1 ; they are independant . Show the mutual independance of Y1=X1/(X1+X2) ; Y2=(X1+X2)/(X1+X2+X3) and Y3 = X1+X2+X3 .
The only thing I've demonstrated is that Y3 is a gamma distribution . Same thing for X1+X2 .
But How can we demonstrated this independance ?
Thank you in advance for your help .