Just to get you started, what is the distribution of N? Then use total expectation:
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 with mean 1. Let be the time the k-th car passes. A turtle needs two minutes to cross the road. Let
(a) Find the expected value of , which is the time until turtle starts to cross, and the expected value of , the time the next car passes
(b) Consider a renewal reward process with if and otherwise. At what rate are rewards earned?"
Thanks a bunch - I really appreciate it!