Random walks with exponential distribution Dembo 5.4.13

Question

How can I go about approaching part a) of this problem?

Answer 1

For $t>0$ we have \begin{align} \mathbb P(S_{\tau_b} - b > t \mid \tau_b = n) &= \mathbb P(S_{\tau_b}>t+b\mid\tau_b=n)\\ &= \mathbb P(\xi_n>t+b\mid \xi_n>b)\\ &= \mathbb P(\xi_n>t)\\ &= e^{-\alpha t}, \end{align} so that $S_{\tau_b}-b$ conditioned on $\{\tau_b=n\}$ has exponential distribution with parameter $\alpha$.

For (b) and (c) I am not sure.