1. The random variable X represents the storm damage to a premises which has encountered a loss. The insurance company handling such claims will pay only W, the excess of the damage over $40,000, for any such damage (i.e., W = X 40,000 if X > 40,000). The payments made by the company in 2005 amounted to: $14,000, $21,000, $6,000, $32,000 and $2,000. Assume that the density function for the damage sustained X takes the form fx(x) = a 2 1040 (20,000 + x)-a-1 for x > 0 where a is an unknown parameter. (a) Determine the density function, mean and variance for W, the typ- ical amount paid by the insurance company (in respect of damage in excess of $40,000 to a premises). (b) Using the method of maximum likelihood, find an estimate of a based on the 2005 data. Give an estimate for the standard error of . (c) Suppose that inflation in 2006 is expected to be 4%. If the excess level remains at $40,000, what is the average amount the company will pay on a storm damage claim over $40,000? 1. The random variable X represents the storm damage to a premises which has encountered a loss. The insurance company handling such claims will pay only W, the excess of the damage over $40,000, for any such damage (i.e., W = X 40,000 if X > 40,000). The payments made by the company in 2005 amounted to: $14,000, $21,000, $6,000, $32,000 and $2,000. Assume that the density function for the damage sustained X takes the form fx(x) = a 2 1040 (20,000 + x)-a-1 for x > 0 where a is an unknown parameter. (a) Determine the density function, mean and variance for W, the typ- ical amount paid by the insurance company (in respect of damage in excess of $40,000 to a premises). (b) Using the method of maximum likelihood, find an estimate of a based on the 2005 data. Give an estimate for the standard error of . (c) Suppose that inflation in 2006 is expected to be 4%. If the excess level remains at $40,000, what is the average amount the company will pay on a storm damage claim over $40,000