A term life insurance policy will pay a beneficiary a certain sum of money upon the death of the policyholder. These policies have premiums that must be paid annually. Suppose an 18- year-old male buys a \($250\),000 1-year term life insurance policy for \($350\). According to the National Vital Statistics Report, Vol. 58, No. 21, the probability that the male will survive the year is 0.998937. Compute the expected value of this policy to the insurance company.

Approach The experiment has two possible outcomes: survival or death. Let the random variable X represent the payout (money lost or gained), depending on survival or death of the insured. Assign probabilities to each payout and substitute these values into Formula (1).

Formula 1

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Mx = [x-P(x)] (1)