Two friends A and B meet every morning at the Grand Central Station around 7 am. Suppose the actual times they arrive are independent and uniformly distributed between 6:55 am and 7:05am. Let Z denote the time between arrivals, i.e. Z = time B arrives - time A arrives (can be negative!).
(a) What is the range of Z?
(b) Find the density of Z.
(c) Find the probability that A waits for at least 5 minutes before B arrives.