A motor insurance portfolio produces claim incidence data for 100,000 policies over one year. The table below shows the observed number of policyholders making 0, 1, 2, 3, 4, 5, and 6 or more claims in a year. No. of claims No. of policies 87,889 11,000 1,000 100 10 26 Total 100,000 (i) Using the method of moments, estimate the parameter of a Poisson distribution to fit the above data and hence calculate the expected number of policies giving rise to the different numbers of claims assuming a Poisson model. [3] (ii) Show that the estimate of the Poisson parameter calculated from the above data using the method of moments is also the maximum likelihood estimate of this parameter. [4] (iii) Using the method of moments, estimate the two parameters of a Type 2 negative binomial distribution to fit the above data and hence calculate the expected number of policies giving rise to the different numbers of claims assuming a negative binomial model. [6] (iv) Explain briefly why you would expect a negative binomial distribution to fit the above data better than a Poisson distribution. [2] [Total 15]The input-output ratio coefficients for a three sector economy are given as: a12 131 0.2 0.3 0.2 A =2 a23 = 0.4 0.1 0.2 while the final demand matrix is given as: a23 232 a33. 0.1 0.3 0.2 10 D = 5 Determine the total output required in each of the three sectors to meet the inter- industry input requirements and the final demand