Imagine you are working for an insurance company. In year 1 there are 100 claims with an average size of $10,000 and in year 2 there are 200 claims with an average size of $12,500. Inflation increases the size of all claims by 10% every year and requires you to adjust the total amount in paid out in $ by 10% each year. (a) A Pareto distribution with a = 3 and 0 unknown is used to model the claim size distribution. Estimate 0 for year 3 using the method of moments. Note that the mean of a Pareto distribution is E(Y) = (0/(@-1)). Next obtain an estimate for the first sample moment Y by calculating the average amount per claim in years 1 and 2 combined after accounting for inflation first in each year. Use this value when you solve for 0 such that you will get a numerical estimate of 0. (b) Assuming a = 3 does not change and neither does the 10% rate of inflation. What amount can you expect the average claim to be in year 3