An underwriter believes that the losses for a particular type of policy can be adequately modelled by a distribution with density function f(x) = cyx¹ exp(-cx¹), x > 0 with unknown parameters c> 0 and y> 0. (a) Derive a formula for the cumulative density function, F(X). (b) Based on a sample of policies the underwriter calculates the lower quartile for the losses as £120 and the upper quartile as £4140. Find the method of percentiles estimates of c and y. (c) Using the estimates of c and 7 found in part (b) to estimate the median loss.
