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A 65 year old couple are considering a joint life insurance policy. The man has a probability of $.90$ of living at least 5 more years, $.95$ for the woman (and assume the event of either person dying is independent of the other). The insurance policy pays $\ 100,000$ if one of them dies and $\ 150,000$ if both die during this time. What is a fair cost for this policy?
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Since their deaths are assumed to be independent,
$P$ (neither dies $)=(.9)(.95)=.855$
$P($ one dies $)=P($ only husband dies $)+P($ only wife dies $)=(.1)(.95)+(.9)(.05)=$ $.14$
$P($ both die $)=(.1)(.05)=.095$
The payout is $0,100000,150000$ respectively in the three cases. The payout is the value the random variable takes. So its expected value is
$E(X)=0(.855)+100000(.14)+150000(.095)=28250$
So a fair price for the policy would be exactly $\ 28,250$, since that is the expected payout.
by Diamond (40,719 points)

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