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Has anyone ever seen a solution for the following...? $$ \left( \frac{1}{n}\sum_{i=1}^{n} x_{i} \right) \times \left( \frac{1}{n} \sum_{i=1}^{n} \frac{1}{x_{i}}\right) $$ where the x values are from a normal distribution with average $ \overline{x} $ and standard deviation $ \sigma_{\overline{x}}$ and n is fairly large (in the millions). I know the answer depends on the ratio $ \frac{\sigma_{\overline{x}}}{\overline{x}}$.

Thanks.

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