Problem 2. (10 points) The arrivals of phone calls at a telephone switching office is a Poisson random process N(t) with an arrival rate of X = 4 calls per second. We monitor N(t) starting from t = 0 over a 10-second interval. Let S be the time of the arrival of the nth call. (You can leave the answer as a function of e). 1. What is P(N(1) = 0), the probability of no phone calls during the first second? (2 points) 2. What is P(N(4) - N(3) = 4), the probability of four phone calls arrive between the third and the fourth second? (2 points) 3. What is E[S10], the expected time that the 10th phone call arrives? (3 points) Hint: consider interarrival time 4. What is Var[S10], the variance of random variable S10? (3 points)