Study guide, I want to make sure I got this question right

(8) Suppose the number of phone calls per hour arriving at an answering service follows a Poisson process with the rate A = 3 (or equivalently, the interarrival times are iid exponential random variables with mean 20 minutes). Circle the correct answer in each of parts (a), (b), (C)- (a) Given that 6 calls arrive in the rst two hours, what is the conditional probability that 4 calls arrive in the second hour? 6 1. 34, 66 (2)27\" 6 3a: '3 a- (b) Let T('i,j) denote the time interval from the with arrival to the jth arrival. Then the correlation between T(1, 3) and T(2, 4) is 0, 1/9, 1/2. (c) Let T(i, j) denote the time interval from the ith arrival to the jth arrival. Then the correlation between T(0, 2) and T(0, 4) is 0, 2 ' 1/2