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