8. The waiting time for a bus at a given station at a certain time of a day is known to have a uniform, U(0, 0), distribution. It is desired to test Ho : 0 12. From other similar routes, it is known that 0 has a Pareto distribution P(5, 3). If the waiting times 10, 3, 2, 5, 8 are observed, calculate the posterior probability of each hypothesis and the Bayes factor. ( You are given the following information: The Pareto P(To, () distribution has a pdf, a+1 f(0|zo, a) = I(20,00) (0 ) To with 0 > To, 0 0. It has mean aro/(a - 1) if a > 1.)