10.1 The number of particles emitted by a radioactive source during a ten second interval has the Poisson(p) distribution. The radioactive source is observed over five 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 p.

i. Find the posterior distribution for p.

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

(b) Suppose Jeffreys’ prior is used for p.

i. Find the posterior distribution for p.

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