(5) A fund has been established for the purpose of insuring 11,060 lives with identical mortality profiles. For each life, you are given:

1. The probability of an accidental death is 0.01, and the probability of a non-accidental death is 0.09
2. If death is accidental, the claim amount is 10. For other causes of death, the claim amount is 1.

Calculate the amount needed in the fund so that the probability, using the normal approximation, is 95% that the fund will be sufficient to pay the death claims.

(Ans 2279)

(1) An insurer has a portfolio of 32 independent policies. The probability of a claim is 1/6. The benefit amount given that there is a claim has a gamma distribution with = 2 and = 6. Let S be the total claims for the portfolio. Using a normal approximation, determine Pr(S>4). (Ans 0.0062)

(3) For three mutually independent integer valued random variables X₁, X₂ and X₃ you are given the following discrete probability functions.

x f₁(x) f₂(x) f₃(x) f₁*f₂(x) f₁*f₂*f₃(x)

0	0.4		y
1	0.6	0.3	0.3	0.42
2	0		.7 - y	0.26	0.272
3	0	0	0

(a) Determine y. (Ans 0.1)

(b) If S = X₁ + X₂ + X₃, determine F_S(4). (Ans 0.928)