I was reading Stochastic Processes (3rd Edition), by J MEDHI Professor Emeritus Guwahati University Guwahati, India, and find the following result without proofs on P25,
Two independent continuous variables $T_1$, $T_2$ are exponential if and only if \begin{align*} Z=\min \left\{T_1, T_2\right\} \text { and } W=T_1-T_2 \end{align*} are independent.
I am thinking how to prove $T_1$ and $T_2$ are exponentials through the independence between $Z$ and $W$. Any reference would be appreciated.
