1. Assume that within a given service game at tennis, successive points form Bernoulli trials with p = P(Server wins) > ½. Tennis rules say that the service game ends as soon as either player has won at least four points, and is at least two points ahead of the other. Find the chances the server wins the game 4-0, 4-1, and 4-2; find also the chance the game reaches 3-3 ("Deuce").
2. Suppose buses arrive at random, at average rate , so that the time to wait follows an Exponential distribution. Show that, conditional on you having already waited time T, without a bus, the remaining time you have to wait is independent of T.