Answer Happy

An insurance company pays out claims via a Poisson process with an average of 5 claims per week. The amount of money per claim is exponentially distributed with mean $500. (a) What is the expected amount paid per year (52 weeks)? [2 marks] (b) What is the standard deviation of the amount paid per year (52 weeks)? [3 marks] (C) What is the covariance of the amount paid over the first two quarters (26 weeks) and the amount paid over the whole year (52 weeks)? [4 marks] (d) If the insurance company has paid 140 claims for a total of $60,000 over the first 26 weeks, what is the amount expected to be paid for the entire year (52 weeks)? [5 marks] (e) An actuary predicts that the claim pattern does not change in the next year. Find the probability that the total claim amount for these 2 years will exceed $250,000. [6 marks)