We assume the following model: St Binomial(12, 0); ~Beta(18, 21); The claim experience for the last 7 years was as follows: x = (7, 9, 8, 3, 3, 7, 8). (a) Calculate the collective premium. (b) Find the parameters x and y of the posterior distribution | S = x. (c) Calculate the Bayesian premium for year 8. (d) The Bayesian premium in (c) can be written as a Credibility Premium. Find the credibility factor z. answer correct to 2 decimals separate your answers with a comma numbers correct to 2 decimals answer correct to 2 decimals answer correct to 2 decimals