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Let $Y = \sum a_iX_i$. In general the cost of computing $\mathbb{E}(|Y|)$ exactly will likely grow exponentially with $n$, because calculating $\mathbb{P}(|Y| = y)$ involves deciding whether there exists a subset of the $a_i$ whose sum is either $y$ or $-y$, which is the NP-complete 0-1 knapsack problem. There are variants of the Central Limit Theorem for ...


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