Math CentralQuandaries & Queries


Question from Katrina, a student:

A term life insurance policy will pay a beneficiary a certain sum of money upon the
death of the policy holder. These policies have premiums that must be paid annually. Suppose a
life insurance company sells a $250,000 one-year term life insurance policy to a 20-year-old male
for $350. According to the National Vital Statistics Report, Vol. 47, No. 28, the probability the
male will survive the year is 0.99865. Compute the expected value of this policy to the insurance
company. Does the company expect to make money at this rate?

Hi Katrina,

To find the expected value of a random variable you take each possible value of the random variable, multiply by the probability of that value occurring and then add them up. One way to look at this problem is to say that the random variable X is the amount of money the insurance company has made or lost on this policy at the end of the year. X has the value $350 if the policy holder lives and X has the value
($350 - $250,000) if the policy holder dies.

Can you complete the problem now?

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