Assignment:
Someone purchases a liability insurance policy, and the probability that they will make a claim on that policy is equal to 0.1. The insurance payout is the amount of money the insurance company must pay if the holder of the policy files a claim. So, if no claim is made, then the insurance payout is just $0; however, whenever a claim is made, the amount of money on the claim, F, has an exponential distribution with mean S 1,000,000. If P is less than the maximum insurance policy payout of $2,000,000, then the insurance payout is equal to F, otherwise, the insurance payout is equal to S2000,000. What is the expected value of the insurance payout? Hint: Consider the indicator of the event "A claim is filed" and how it can be used to compute the expectation in question.
Provide complete and step by step solution for the question and show calculations and use formulas.