IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
Given Λ = λ, the claim count N is Poisson(λ). Λ has an exponential distribution with mean 2. What is Var(N)?
Var(N) = 6. The expected conditional variance is E[Λ]=2, and the variance of the conditional mean is Var(Λ)=4 for an exponential with mean 2. Their sum is 6.
- A2
- B4
- C6Correct
- D8
- 10
Explanation
E[Var(N|Λ)] = E[Λ] = 2. Var(E[N|Λ]) = Var(Λ) = 2² = 4 for an exponential with mean 2. Total = 6. Option 4 ignores the process variance.
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