Statistics Graduate Level Quiz
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An insurance portfolio has a random claim intensity. Conditional on Λ\Lambda, the number of claims NN is Poisson with mean Λ\Lambda. The mixing variable satisfies E[Λ]=3E[\Lambda]=3 and Var(Λ)=2Var(\Lambda)=2. Claim amounts X1,X2,…X_1,X_2,\ldots are independent of NN and Λ\Lambda, with E[Xi]=2E[X_i]=2 and Var(Xi)=5Var(X_i)=5.
If the aggregate loss is S=∑i=1NXiS=\sum_{i=1}^{N}X_i, what is Var(S)Var(S)?
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