Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.m. on a particular day. In fact, Allison is equally likely to arrive at exactly 1 p.m., 2 p.m., 3 p.m., 4 p.m., 5 p.m., or 6 p.m. Teri is also equally likely to arrive at each of these six times, and Allison's and Teri's arrival times are independent of one another. Thus there are 36 equally likely (Allison, Teri) arrival-time pairs, for example, (2, 3) or (6, 1). Suppose that the first person to arrive waits until the second person arrives; let w be the amount of time the first person has to wait.
a. What is the probability distribution of w?
b. On average, how much time do you expect to elapse between the two arrivals?