The number of particles emitted by a radioactive source during a ten second interval has the Poisson( ) distribution. The radioactive source is observed over ve non-overlapping intervals of ten seconds each. The number of particles emitted during each interval are: \(4,1,3,1,3\).

(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?