Question: "Traffic on Snyder Hill Road is a Poisson process with rate 1 car per minute. That is, the times between cars are independent exponentials $\displaystyle t_1, t_2, . . .$ with mean 1. Let $\displaystyle T_k = t_i + ... + t_k$ be the time the k-th car passes. A turtle needs two minutes to cross the road. Let $\displaystyle N = min\{i : t_i > 2\}$

(a) Find the expected value of $\displaystyle T_{N-1}$, which is the time until turtle starts to cross, and the expected value of $\displaystyle T_N$, the time the next car passes

(b) Consider a renewal reward process with $\displaystyle r_i = 1$ if $\displaystyle t_i > 2$ and $\displaystyle r_i = 0$ otherwise. At what rate are rewards earned?"

Thanks a bunch - I really appreciate it!