A show is scheduled to start at 9: 00 a.M., 9: 30 A.M. and 10: 00 A.M. Once the show starts, the gate will be closed. A visitor will arrive at the gate at a time uniformly distributed between 8: 30 a.m. and 10: 00 A.M. Determine the following:
(a) Cumulative distribution function of the time (in minutes) between arrival and 8: 30 A.M.
(b) Mean and variance of the distribution in the previous part
(c) Probability that a visitor waits less than 10 minutes for a show
(d) Probability that a visitor waits more than 20 minutes for a show
