Question

A life insurer has created a special one-year term policy for a couple that travels to high-risk locations. The policy pays nothing if neither die during the year, 100000 if exactly one dies, and k if both die. You are told that the standard deviation for the payout is 74000. Find the expected value of the payout is 74000. Find the expected value of the payout for the year on this policy.

(I dont know where to start, should I start with V(x) = Ex^2 - Ex ^2?)

Answer 1

Probability of no die rightarrow $ 0 Pays Probability of one die rightarrow $ 100,000 Probability of both die rightarrow $ k > 0 P(atleast one die) = 0.1 (given) = P(one dies) + P(both dies) Therefore P(exactly one dies) = 0.08 (given) P(both dies) = 1 - 0.08 = 0.02 Expected pay off = P(nodie) times $0 + P(one die) times 100000 + P(both die) times $ k = 0 + (0.08) (100000) + (0.02) (k) = 8000 + 0.02 k Here k accounts the standard deviation i.e 74000 Therefore expected payoff = 8000 + 0.02 times 74000 = 8000 + 1480 = 9480