14. A regional telephone company is analyzing the number of telephone calls that are connected to wrong numbers at its telephone exchange. It collects the number of wrong telephone connections on each of 200 days, and treats the observations as the outcome of a random sample of size 200 from a Poisson population distribution:

fðz; lÞ ¼ el lz z! If0;1;2;:::g ðzÞ

(a) Define the MLE of l, the expected number of wrong connections per day.

(b) Is the MLE the MVUE for l? Is it consistent? Asymptotically normal? Asymptotically efficient?