IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
The number of claims N is binomial with n = 10 and p = 0.3. Claim sizes are independent with mean 100 and variance 400, independent of N. What is Var(S) for aggregate claims S?
The working gives 22,200, which is not among the options, so the question is flawed.
- A30,000
- B24,000
- C21,000
- D27,000Correct
- 33,000
Explanation
E[N]=3, Var(N)=10x0.3x0.7=2.1. Var(S)=E[N]Var(X)+Var(N)E[X]^2=3x400+2.1x10,000=1,200+21,000=22,200. This is not among the options, so the question is flawed.
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