IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
An insurer has N geometric-type claim counts with E[N] = 4 and Var(N) = 12. Claim sizes have mean 10 and variance 20. What is Var(S)?
Var(S) is 1,280. Using E[N]Var(X) + Var(N)E[X]², we get 4×20 = 80 plus 12×100 = 1,200, totalling 1,280.
- A1,280Correct
- B80
- C1,200
- D400
- 1,040
Explanation
Var(S) = E[N]Var(X) + Var(N)E[X]² = 4×20 + 12×100 = 80 + 1,200 = 1,280. Option 1,200 omits the claim-size variance term.
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