11.11 Suppose I want to cross a road with no stopping sign. On that road, cars pass according to a Poisson process with rate λ. I need at least a τ second gap to cross the road safely. If I observe a gap of at least τ seconds, I start crossing immediately. Let T the amount of time I need to wait until I start crossing.

a) Set up a renewal equation for P(T

b) Find E[T] + τ, the expected time to cross the road.