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A life insurer has created a special one-year term insurance policy for a pair of business people who travel to high risk locations. The insurance policy pays nothing if neither die in the year, $\$1,000,000$ if exactly one of the two die, and $K > 0$ if both die. The insurer determines that there is a probability $0.1$ that at least one of the two will die during the year and a probability of $0.08$ that exactly one of the two will die during the year. You are told that the standard deviation of the payout is $\$74,000$. Find the expected payout for the year on this policy.

I found $E[X]$ to be $0.02K + 8000$ and $E[X^2]$ to be $800, 000, 000 + 0.02K^2 $ but Im stuck here. Am I complete off or am I just missing something?

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  • $\begingroup$ Standard deviation $\sigma$ = $\sqrt{Var(X)}$, and $Var(X) = E[X^2] - E[X]^2$. You might be able to use this fact to solve. $\endgroup$ – Trent Bing Nov 17 '15 at 20:13
  • $\begingroup$ Ugh, completely forgot we were given that information. Thanks! $\endgroup$ – rachel Nov 17 '15 at 20:18

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