An insurance agent sells a policy which has a $100 deductible and a $5000 cap. This means that when the policy holder files a claim, the policy holder must pay the first $100. After the first $100, the insurance company pays the rest of the claim up to a maximum payment of $5000. Any excess must be paid by the policy holder. Suppose that the dollar amount X of a claim has a continuous distribution with p.d.f. f (x) = 1/(1+ x)2 for x >0 and 0 otherwise. Let Y be the amount that the insurance company has to pay on the claim.
a. Write Y as a function of X, i.e., Y = r(X).
b. Find the c.d.f. of Y.
c. Explain why Y has neither a continuous nor a discrete distribution.