At a facility’s loading dock, delivery vehicles arrive randomly, starting at 8:00 AM, at a rate of 2.0 per hour. If the dock is occupied by another vehicle, the driver must park in a waiting area until the dock is clear; this occurs with probability 0.20, independent of the time of day or other variables. Identify the family and parameter(s) of each of the following random variables (for instance, “Bernoulli(0.5)”). If it is not one of our “famous” families indicate “other”; if the parameters cannot be determined indicate so.
(a) The time elapsed before the next vehicle arrives. (b) The number of arrivals between 8:00 AM and 10:00 AM. (c) The number of vehicles in the loading dock. (d) Of the next 10 deliveries to arrive, the number than have to wait for the dock to clear. (e) The number of vehicles in the waiting area. (f) The number of deliveries made up to and including the ﬁrst that has to wait for the dock to clear. (g) The arrival time of the third delivery on a given day.