If X and Y be two independent Gamma variates with parameters $\displaystyle \mu$ and v respectively,show that the variables U=X+Y and $\displaystyle \frac{X}{X+Y}$ are independent and that U is a $\displaystyle (\mu+v)$variate and V is a $\displaystyle \beta_1(\mu,v)$ variate.

How can we use the jacobian transformation to solve this question.