IAI Actuarial Core Principles · Actuarial Statistics · Generating functions
Annual claim numbers N for a portfolio are Poisson with mean 10. Individual claim amounts X are independent of N with E[X] = 4 and Var(X) = 12 (in ₹ thousand and its square). What is Var(S) for aggregate claims S?
Var(S) is 280. For a compound Poisson distribution the variance equals λE[X²], where E[X²] = 12 + 16 = 28, so 10 × 28 = 280.
- A280Correct
- B120
- C160
- D40
- 400
Explanation
For a compound Poisson, Var(S) = λE[X²]. E[X²] = Var(X) + E[X]² = 12 + 16 = 28. So Var(S) = 10 × 28 = 280. Option B uses only λVar(X), missing the mean term. Option C uses E[N]Var(X) + ... with wrong values.
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