An office manager feels that for a certain kind of business the daily number of incoming telephone calls is a random variable having a Poisson distribution, whose parameter has a prior gamma distribution with α = 50 and β = 2. Being told that one such business had 112 incoming calls on a given day, what would be her estimate of that particular business’s average daily number of incoming calls if she considers

(a) Only the prior information;

(b) Only the direct information;

(c) Both kinds of information and the theory of Exercise 10.77?