An insurer assumes that the number of claims, N, in one month from a particular type of policy follows the distribution: P(N = 0) = 0, P(N = 1) = 1 – 0. Prior beliefs on the parameter are represented by a beta distribution with density function ƒ(0) = 2(1 – 0), 0 ≤ 0 ≤ 1 There are a total of 10 claims on this policy over a 16 month period. The claims are assumed to arise independently. (a) Derive the posterior distribution for 0. [4 marks] (b) Determine the Bayesian estimate for under all-or-nothing loss. [3 marks]
