ThmDex – An index of mathematical definitions, results, and conjectures.
Proof P3561 on R5229: Bessel-corrected sample variance of independent standard gaussians is a transformed chi-squared random real number
P3561
By definition, we have \begin{equation} \chi \overset{d}{=} \sum_{n = 1}^N Z^2_n \end{equation} whence the result follows. $\square$