An insurance policy issued to the boat owner has deductible amount of $1000, so the amount of damage claimed should exceed this deductible before there will be payout. Assume the amount (1000s of dollars) of randomly selected claim is continuous random variable with pdf f(x)=3/x^4 where x>1. Consider a random sample of three claims.
a) What is the probability that at least one of the claim amounts exceeds $5000?
b) What is the expected value of the largest amount claimed?