(a) Find an invertible transformation $S^{(n)}=T\left(X^{(n)} ight)$ that relates the $n$ epoch times $S^{(n)}=\left(S_{1}, \ldots, S_{n} ight)$ to the inter-arrival times $X^{(n)}=\left(X_{1}, \ldots, X_{n} ight)$. (b) What is the joint $\operatorname{PDF} f_{X^{(n)}}\left(x^{(n)} ight)$ ? (c) Using the above remark find another proof for $$ f_{S^{(n)}}\left(s^{(n)} ight)=\lambda^{n} e^{-\lambda s_{n}} $$