= Random sum of independent claims
{title2=$\mathbb ES=\mathbb EN\,\mathbb EX$}
For independent claim sizes with common <expected value> $m$ and <variance> $v$, independent of the nonnegative integer count $N$, the aggregate satisfies $\mathbb ES=m\mathbb EN$ and $\operatorname{Var}(S)=v\mathbb EN+m^2\operatorname{Var}(N)$. Its <moment-generating function> is $G_N(M_X(t))$ wherever finite. These identities follow from the <law of total expectation> and <law of total variance>.
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