The number of claims received by an insurance company during a week follows a Poisson ( ) distribution. The weekly number of claims observed over a ten week period are: \(5,8,4,6,11,6,6,5,6,4\).

(a) Suppose a prior uniform distribution is used for

i. Find the posterior distribution for .

ii. What are the posterior mean, median, and variance in this case?

(b) Suppose Je reys' prior is used for

i. Find the posterior distribution for .

ii. What are the posterior mean, median, and variance in this case?