4. There are two types of calls to the Dalseong chicken delivery house. Menu A calls arrive as a Poisson process with rate 2A= 1. Menu B calls arrive as an independent Poisson process with rate AB = 2. Let us fix t to be the time that you started to solve this homework. (a) What is the expected length of the interval that t belongs to? That is, the interval from the last call before t until the first call after t. (b) What is the probability that t belongs to an AA interval? That is, the first event before, as well as the first event after time t are both of menu A. (c) What is the probability that between t and t+1, we have exactly two events, one of menu A, followed by one of menu B? (d) Suppose that a menu B call just arrived. Find the expected time until the end of the first future AA interval? (Hint: Construct a Markov chain with states of A, B and END. The END state is for the end of the first future AA interval. Then, find a pair of equations for the expected time to the END state starting from the A state and the B state.)