1 Shuttles and Taxis at Airport In front of terminal 3 at San Francisco Airport is a pickup area where shuttles and taxis arrive according to a Poisson process. The shuttles arrive at a rate ll = 1/20 (i.e. l shuttle per 20 minutes) and the taxis arrive at a rate Ag 2 1/ 10 (i.e. 1 taxi per 10 minutes) starting at 00:00. The shuttles and the taxis arrive independently. (a) What is the distribution of the following: (i) The number of taxis that arrive between times 00:00 and 00:20? (ii) The number of shuttles that arrive between times 00:00 and 00:20? (iii) The total number of pickup vehicles that arrive between times 00:00 and 00:20? (b) What is the probability that exactly 1 shuttle and 3 taxis arrive between times 00:00 and 00:20? (0) Given that exactly 1 pickup vehicle arrived between times 00:00 and 00:20, what is the condi- tional probability that this vehicle was a taxi? ((1) Suppose you reach the pickup area at 00:20. You learn that you missed 3 taxis and l shuttle in those 20 minutes. What is the probability that you need to wait for more than 10 mins until either a shuttle or a taxi arrives