1. A fair coin is tossed once and X is defined to be 1 if the coin lands heads and 2 if it lands tails. Let W be the waiting time for X arrivals in a Poisson process with average rate . Find the p.d.f. of W.

2. Airplanes land in a certain busy airport according to a Poisson process with an average rate of 2 planes per minutes. (a) Evaluate the probabilities of the following two events: A: 10 cars planes lend in the next 5 minutes. B: exactly 2 airplanes lend every minute for the next 5 minutes (b) Evaluate in two different ways the probability that the time until the next plane (beginning from this moment) exceeds 3 minutes.