Problem: Life insurance
(a) It would be quite risky for you to insure the life of a 21-year-old friend. There is a high probability that your friend would live and you would gain $1250 in premiums. But if he were to die, you would lose almost $100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.
(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring a single person's life by computing the standard deviation of the income Y that the insurer will receive. Find sY using the distribution and mean found.