Let $Z_1, Z_2, Z_3, \dots \in \text{Gaussian}(0, 1)$ each be a D211: Standard gaussian random real number such that

(i)	$Z_1, Z_2, Z_3, \dots$ is an D2713: Independent random collection

A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is a chi random real number with parameter $N \in 1, 2, 3, \ldots$ if and only if \begin{equation} X \overset{d}{=} \left( \sum_{n = 1}^N Z^2_n \right)^{1/2} \end{equation}

Let $Z_1, Z_2, Z_3, \dots \in \text{Gaussian}(0, 1)$ each be a D211: Standard gaussian random real number such that

(i)	$Z_1, Z_2, Z_3, \dots$ is an D2713: Independent random collection

A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is a chi random real number with parameter $N \in 1, 2, 3, \ldots$ if and only if \begin{equation} X \overset{d}{=} \sqrt{ \sum_{n = 1}^N Z^2_n } \end{equation}