The random variables $X_{1}$ and $X_{2}$ are independent, and each has an exponential distribution with parameter $\lambda$. Find the joint density function of

$$Y_{1}=X_{1}+X_{2}, \quad Y_{2}=X_{1} / X_{2}$$

and show that $Y_{1}$ and $Y_{2}$ are independent. What is the density of $Y_{2}$ ?