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.