Processing math: 100%
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
Formulation 0
Let Z1,Z2,Z3,Gaussian(0,1) each be a D211: Standard gaussian random real number such that
(i) Z1,Z2,Z3, is an D2713: Independent random collection
A D3161: Random real number XRandom(R) is a chi-squared random real number with parameter N{1,2,3,} if and only if Xd=Nn=1Z2n
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