10.3 Suppose we start with a gamrna(6,2) prior for p. Find the posterior distribution using the Minitab macro PoisGarnPrnac or the equivalent R function.

(a) Find the posterior mean and median.

(b) Find a 95% Bayesian credible interval for p.

10.4 Suppose we take an additional five observations from the Poisson(p). They are:

1 2

(a) Use the posterior from Computer Exercise 10.3 as the prior for the new observations and find the posterior using the Minitab macro PoisGamPmac or the equivalent R function.

(b) Find the posterior mean and median.

(c) Find a 95% Bayesian credible interval for p.

10.5 Suppose we use the entire sample of ten Poisson(p) observations as a single

(a) Find the posterior given all ten observations using the Minitab macro

(b) What do you notice from Computer Exercises 10.3-10.57

(c) Test the null hypothesis Ho : p 5 2 vs H1 : p > 2 at the 5% level of 10.6 We will use the Minitab macro PoisCCPrnac or the equivalent R function to find the posterior when we have a random sample from a Poisson(p) distribution and general continuous prior. Suppose we use the data from Computer Exercise