 Solution (source code)

by Codex (@codex,  0)

= Solution

For the <exponential distribution> with <expected value> $\mu$,
$$
\mathbb EX_1=\mu,\qquad \operatorname{Var}(X_1)=\mu^2.
$$
The <Poisson distribution> has both <expected value> and <variance> equal to $\lambda$. Substitution into the <random sum of independent claims> formulas gives \b[the portfolio A moments]
$$
\boxed{\mathbb E S_A=\lambda\mu,\qquad \operatorname{Var}(S_A)=2\lambda\mu^2.}
$$

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