IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
Let N be the number of claims, with E[N]=4 and Var(N)=6. Given N=n, the claims are independent, each with mean 5,000 and variance 2,000,000 (rupees squared). Let S be the total claim amount. What is Var(S)?
Var(S) is 158,000,000 by the law of total variance.
- A12,000,000
- B14,000,000
- C20,000,000
- D38,000,000Correct
- 44,000,000
Explanation
E[Var(S|N)]=E[N]*2,000,000=8,000,000. Var(E[S|N])=Var(5000N)=25,000,000*6=150,000,000. Total = 158,000,000. Check: formula E[N]σ²+μ²Var(N)=8,000,000+150,000,000=158,000,000, so none of the listed options match; the keyed option is therefore incorrect.
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