Suppose we face a lossLthat is exponentially distributed with mean$10,000. We purchase an insurance policy against this loss with a $5,000 deductible. The premium charged by the insurance companyis twice their expected payout.

(a) What is the median loss?

(b) What is the probability that the insurance company will have topay a claim on this policy?

(c) What is the expected loss given that the loss is greater than$25,000?

(d) Give an expression for the amount that the insurance companypays on claims against this policy.

(e) Compute the expected amount that the insurance company payson claims against this policy.

(f) What is the premium charged by the insurance company for thispolicy?

(g) What is the probability that the insurance company loses moneyon this policy?