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Suppose that you are trying to estimate some quantity $\mu$ by performing some random experiment $X$ with mean $\mu$ and variance $\sigma^2$. In order to obtain a better estimate, you can repeat the experiment $n$ times and take the average $\bar{X} = \frac{X_1+\cdots+X_n}{n}$, which also has mean $\mu$ but its variance is only $\sigma^2/n$. This means that $...

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