Cars pass a certain street location according to a Poisson process with rate . A woman who

Cars pass a certain street location according to a Poisson process with rate λ. A woman who wants to cross the street at that location waits until she can see that no cars will come by in the next T time units.

(a) Find the probability that her waiting time is 0.

(b) Find her expected waiting time.

Hint: Condition on the time of the first car.