5. (a) Assume that the following data set 70, 75, 80, 85, 90, 90, 95, 98, 100, 100 represents the insurance payments after a maximum covered loss of u = 120 and an ordinary deductible of d = 20 is applied. At a 5% significance level, use the Kolmogorov-Smirnov test to determine whether an exponential distribution is a plausible model for this data. [10 marks] Note: Critical values for the Kolmogorov-Smirnov test are: 1.22/√n, 1.36/√√n and 1.63/√√n at 10%, 5% and 1% levels respectively. (b) Each day, for 365 days, the number of claims is recorded. The results were 160 days with no claims, 79 days with one claim, 69 days with two claims, 50 days with three claims, 5 days with four claims, 2 days with five claims, and no days with six or more claims. For a Poisson model with mean A, determine the maximum likelihood estimate of A and then perform the chi-square goodness-of-fit test at 5% significance level using the maximum number of groups such that each group has at least five expected observations. [10 marks]