1. Given the following car insurance annual claim data of a particular policy- holder (k+1) 3 39 5 11 6 5 2 where k is y

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1 Given The Following Car Insurance Annual Claim Data Of A Particular Policy Holder K 1 3 39 5 11 6 5 2 Where K Is Y 1 (55.04 KiB) Viewed 19 times

1. Given the following car insurance annual claim data of a particular policy- holder (k+1) 3 39 5 11 6 5 2 where k is your second to last digit of your student ID number. The individual claim amount X, is an exponential random variable with unknown parameter A. It is known that the parameter A follows the gamma distribution over the collective, i.e. A has the density fA (A) = (28+6)/e-2(+3) >0, where B is your last digit of your student ID number. (a) Write down the values of k and 3. Derive the posterior predictive density of a new sample Y from the same policyholder. Which distribution does it follow? [6 marks] (b) Find the Bayesian estimate for the unknown parameter A when the quadratic loss function is used. Find the estimate which maximises the posterior density of A. [6 marks) (c) Find the Bayes premium PBayes for this policyholder. Is the Bülhmann credibility premium Pcred equal to the Bayes premium? [9 marks]