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Definition D4864
Chi random unsigned real number

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 $$X \overset{d}{=} \left( \sum_{n = 1}^N Z^2_n \right)^{1/2}$$

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 $$X \overset{d}{=} \sqrt{ \sum_{n = 1}^N Z^2_n }$$
Children
 ▶ Chi-squared random unsigned real number