Suppose we start with a Je reys' prior for the Poisson parameter . [ g()=quad frac{1}{2} ]

Question:

Suppose we start with a Je reys' prior for the Poisson parameter .

\[
g()=\quad \frac{1}{2}
\]

(a) What gamma( $r v)$ prior will give this form?

(b) Find the posterior distribution using the macro PoisGamP in Minitab or or the function poisgamp in $\mathrm{R}$.

(c) Find the posterior mean and median.

(d) Find a 95\% Bayesian credible interval for .