Exercise 5. There are two types of calls to the UCLA Campus Patrol. Type A calls (distress calls) arrive as a Poisson process with rate A. Type B calls (professors who have lost their keys) arrive as an independent Poisson process with rate Ap. Let us fix t to be 12 o'clock. (1) What is the expected length of the interval that t belongs to? (That is, the interval from the last event before t until the first event after t.) (2) What is the probability that t belongs to an AA interval? (That is, the first event before, as well as the first event after t are both of type A.) (3) Let c be a constant. What is the probability that between t and t + c, we have exactly two events, one of type A, followed by one of type B