Problem 3 A dolphin show is scheduled to start at 9:00 a.m., 9:30 a.m., 10:00 a.m. and 10:30 a.m. Once the show starts, the gate will be closed. A visitor will arrive at the gate at a time (continuous) uniformly distributed between 8:30 a.m. and 10:30 a.m. and will see the first possible show after his/her arrival. Arrival times of different visitors are independent random variables. a) Determine the cumulative distribution function of the time (in minutes) between arrival and 8:30 a.m. b) Determine the probability that a visitor waits less than 10 minutes for a show. c) Determine the probability that a visitor waits more than 20 minutes for a show. d) Determine the probability that from 10 arbitrary visitors two see the 9:00 a.m. show.