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"Given certain conditions, the mean of a sufficiently large number of iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed" ([Wikipedia](http://en.wikipedia.org/wiki/Central_limit_theorem)).

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The classical central limit theorem states that if $X_1, X_2, \ldots, X_n$ are IID random variables with mean $\mu$ and standard deviation $\sigma$, then ${\lim}_{n \rightarrow \infty} \frac{\frac{1 …
asked Sep 23 '16 by Christian
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Let $\overline{X} = \frac{1}{n} \sum_{i=1}^n X_i$, and $S^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \overline{X})^2$. It is well known that if the $X_i$ are IID normals, say $X_i \sim N(\mu, \sigma)$, th …
asked Dec 28 '16 by Christian