Generate a Poisson P() sample by R codes: set.seed(1107); n<-200; X<-rpois(n, 2)

Assume that the mean > 0 is the unknown parameter, use the Jeffreys prior to answer the following questions.

(a) Find the 90% ET and HPD credible intervals of , respectively. What are the actual size of the HPD interval, the density value at the cut points, and the probabilities at two tails?

(b) Find the point estimates of by the methods of MMSE, MAPE and MED, respectively.

(c) Compare your results in parts (a) and (b), with corresponding MME and MLE results.