Prove that if the variables \(\xi\) and \(\eta\) are independent and their density function is

\[ p_{\xi}(x)=p_{\eta}(x)=\left\{\begin{array}{cc} 0 & \text { for } x<0 \\ e^{-x} & \text { for } x>0 \end{array}\right. \]

then the variables \(\xi+\eta\) and \(\frac{\xi}{\eta}\) are also independent.