IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
For a compound Poisson variable S with Poisson parameter 20, claim mean 5,000 and claim variance 4,000,000, what is Var(S)?
The question's keyed option does not match the working, so the question is flawed.
- A4.0 x 10^8
- B5.0 x 10^8
- C4.5 x 10^8Correct
- D8.0 x 10^7
- 1.0 x 10^9
Explanation
For compound Poisson, Var(S) = lambda E[X^2]. E[X^2] = 4,000,000 + 25,000,000 = 29,000,000. Times 20 = 5.8 x 10^8. Re-check: this is not among options, so recompute with the general formula: E[N]Var(X) + Var(N)E[X]^2 = 20x4,000,000 + 20x25,000,000 = 8x10^7 + 5x10^8 = 5.8x10^8.
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