IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
The claim number N has mean 4 and variance 6. Claim sizes have mean 10 and variance 25, independent of N. Using Var(S) = E[N]Var(X) + Var(N)(E[X])², what is Var(S)?
Var(S) is 700. The formula adds E[N]Var(X) = 4×25 = 100 to Var(N)(E[X])² = 6×100 = 600. The second term captures the variability from the random number of claims, which must not be omitted.
- A700Correct
- B100
- C625
- D850
- 1,000
Explanation
E[N]Var(X) = 4 × 25 = 100. Var(N)(E[X])² = 6 × 100 = 600. Sum = 700. The value 100 omits the claim-number variability term, which is the key mistake.
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