# Category:Student's t-Distribution

Jump to navigation
Jump to search

This category contains results about Student's $t$-distribution.

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$.

$X$ is said to have a **$t$-distribution** with $k$ degrees of freedom if it has probability density function:

- $\map {f_X} x = \dfrac {\map \Gamma {\frac {k + 1} 2} } {\sqrt {\pi k} \, \map \Gamma {\frac k 2} } \paren {1 + \dfrac {x^2} k}^{-\frac {k + 1} 2}$

for some $k \in \R_{> 0}$.

This is written:

- $X \sim \StudentT k$

## Pages in category "Student's t-Distribution"

The following 5 pages are in this category, out of 5 total.