An insurance company has a portfolio of policies under which individual loss amounts follow an exponential distribution with mean 1/2. There is an individual excess of loss reinsurance arrangement in place with retention level 100. In one year, the insurer observes: 85 claims for amounts below 100 with mean claim amount 42; and 39 claims for amounts above the retention level. [5] 0) Calculate the maximum likelihood estimate of 2. (ii) Show that the estimate of a produced by applying the method of moments to the distribution of amounts paid by the insurer is 0.011164. 15]