SOA Exam FAM Sample Question 41
Study guide: Exam FAM
For a collective risk model the number of losses, N, has a Poisson distribution with \lambda = 20.
The common distribution of the individual losses has the following characteristics:
(i) E[X] = 70
(ii) E[X \wedge 30] = 25
(iii) \Pr(X > 30) = 0.75
(iv) E[X^2 \mid X > 30] = 9000
An insurance covers aggregate losses subject to an ordinary deductible of 30 per loss.
Calculate the variance of the aggregate payments of the insurance.
- A) 54,000
- B) 67,500
- C) 81,000
- D) 94,500
- E) 108,000
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