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#1
12-21-2011, 01:16 PM
 Ionic Order Member CAS SOA Join Date: Jan 2011 Location: Seattle Posts: 1,259
Question about compound variance (aggregate loss models)

ASM section 14.2 (11th edition) shows the derivation of the compound variance formula from the conditional variance formula. I understand all of the steps, except this one:

$E_N[Var_X(X)]=Var_X(X)$ only if X is independent of N, where N is the number of claims and X is the size of each claim

I think I'm missing a very fundamental rule in probability here, but I can't remember which one is it. Any ideas?