ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Collection of sets ▼ Set union ▼ Successor set ▼ Inductive set ▼ Set of inductive sets ▼ Set of natural numbers ▼ Set of integers ▼ Set of rademacher integers ▼ Rademacher integer ▼ Rademacher random integer ▼ Standard rademacher random integer ▼ Standard gaussian random real number ▼ Chi random unsigned real number
Definition D212
Chi-squared 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-squared random real number with parameter $N \in \{ 1, 2, 3, \ldots \}$ if and only if $$X \overset{d}{=} \sum_{n = 1}^N Z^2_n$$
Children
 ▶ D4865: Fisher random unsigned real number ▶ D5285: Standard chi-squared random unsigned real number
Results
 ▶ R5230: Bessel-corrected sample variance of I.I.D. gaussians is a transformed chi-squared random real number ▶ R5229: Bessel-corrected sample variance of independent standard gaussians is a transformed chi-squared random real number ▶ R5435: Expectation of a chi-squared random unsigned real number