consider the following model for aggregate claim amounts S:(adsbygoogle = window.adsbygoogle || []).push({});

S=X1+X2+.....+XN

where the Xi are independent, identically distributed random

variables representing individual claim amounts and N is a random

variable,independent of the Xi and representing the number of

claims.let X has ìx and let N has mean ìN and variance ó²N.

a) show that E(SN)=ìX ( ì²N + ó²N ) by considering expected values

conditional on the value of N

b) hence derive an expression for the covariance between S and N.

I know that

E(S) = E(E(S|N)) = E(N)E(S) = ìXìN,

Var(E(S|N)) = Var(N)Var(S) = ó²Xó²N

but how to link it with E(SN)??

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# Aggregate model

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