Question 1
Let $X_1$ and $X_2$ be independent random variables each having the probability distribution
$f(x) = \begin{cases} e^{-x}, & x > 0, \\ 0, & \text{elsewhere.} \end{cases}$
Show that the random variables $Y_1$ and $Y_2$ are independent when $Y_1 = X_1 + X_2$ and $Y_2 = \frac{X_1}{X_1+X_2}$.
