# What is the product of the average x and the average (1/x), where x is normally distributed.

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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