Suppose that the number of customers per hour arriving at a Starbucks store follows a Poisson process. Let Xt denote the number of customers who arrive by time t > 0 [as usually we assume that Xo = 0]. Let Y and Y2 denote the waiting time for the first and the second customer, respectively. Suppose that we know that the expected waiting time for the first customer is 1/3 hour [that is E(Y1) = 1/3]. (a) Compute the probability that 8 customers arrived in the first three hours. (b) Given it is known that exactly 3 customers arrived in the first hour. What is the probability that exactly 5 customers arrived in the first two hours? (c) Compute the expected value E(Y1Y2). (d) Compute E(X1X5|F2)