Math CentralQuandaries & Queries


Question from Lara, a student:

A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old male for $350. According to the National Vital Statistics Report the probability that the male survives the year is 0.998734. Compute and interpret the expected value of this policy to the insurance company.
I'm very confused on how to do this. I assume x is the profit the insurance company makes in the year of $350 but beyond that I don't know what to do. Thanks.

Hi Lara,

I think that what is expected is to let the random variable X be the amount that the insurance company pays to the policy holder during the year. The value of X is either $\$0$ with a probability of 0.998734 or $\$250,000$ with a probability of 1 - 0.998734. What is the expected value of X?


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