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Beni Cherniavsky-Paskin Updated test.tex through Banyan.
over 10 years ago
Commit id: d0e0fd1f565c0c8d16c204ac993d9b1f8e996438
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\subsection{Mathematics}
\LaTeX{} is great at typesetting mathematics. Let
$X_1, X_2, $X_3, X_5, \ldots, X_n$ be a sequence of independent and identically distributed random variables with $\text{E}[X_i] = \mu$ and $\text{Var}[X_i] = \sigma^2 < \infty$, and let
$$S_n = \frac{X_1 + X_2 + \cdots + X_n}{n}
= \frac{1}{n}\sum_{i}^{n} X_i$$
denote their mean. Then as $n$ approaches infinity, the random variables $\sqrt{n}(S_n - \mu)$ converge in distribution to a normal $\mathcal{N}(0, \sigma^2)$.