# Student's T-Distribution

A probability distribution $$T(\nu)$$ governing the normalised difference between the mean $$\mu$$ of a normal distribution $$N(\mu, \sigma)$$ and the mean of a set of $$n$$ independent observations of it, defined by the random variable
$t = \frac{\mu^\prime - \mu}{n^{-\frac12} \times s}$
where
\begin{align*} n &= \nu + 1\\ Z_i &\sim N(\mu, \sigma)\\ \mu^\prime &= \frac{1}{n} \times \sum_{i=0}^{n-1} Z_i\\ s^2 &= \frac{1}{n-1} \times \sum_{i=0}^{n-1} \left(Z_i - \mu^\prime\right)^2 \end{align*}
$$\sim$$ means drawn from and $$\sum$$ is the summation sign.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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