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 21 = 1/20 (i.e. 1 shuttle per 20 minutes) and the taxis arrive at a rate 22 = 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