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.