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(a) (i) Describe two features of short-term insurance contracts. [3] (ii) Suggest two examples of short-term insurance contracts. [2] (b) The annual aggregate claim amount, S, arising on a short-term insurance portfolio follows a compound Poisson distribution with parameter 5. Individual claim amounts follow a twoparameter Pareto distribution with parameters and . A sample of individual claim amounts was taken and the sample mean and standard deviation were 10,000 and 15,000 , respectively. (i) Estimate the parameters of the Pareto distribution of the individual claim amounts using the method of moments. [8] (ii) Determine the variance and the third central moment of S, using the estimated Pareto parameters from part (i). [10]