SOA Question 50

50. A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. Calculate the expected amount paid to the company under this policy during a one-year period.

(A) 2,769

(B) 5,000

(C) 7,231

(D) 8,347

(E) 10,578



The solution does not make sense to me, because I'm apparently not understanding something conceptually.



I just think about it logically. 0 storms, the policy pays nothing. 1 storm, the policy pays nothing. 2 or more storms, the policy pays something. What are the probabilities of more than 1 storm? Well,



X P(X) Expected payout of the policy

2 .251 5020

3 .1254 2508

4 .047 1410



Well, we're already above all values outside E, but the correct answer is C. How is that the correct answer? Just with X = 2 and X = 3 we already have paid more than that. Why does the solution have us taking out 10000 randomly? I understand P(0) and P(1) are not zero, but the policy pays nothing under either condition, so the expected payout is 0 for both

SOA Question 50