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ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
▼
Set of symbols
▼
Alphabet
▼
Deduction system
▼
Theory
▼
Zermelo-Fraenkel set theory
▼
Set
▼
Collection of sets
▼
Set union
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Successor set
▼
Inductive set
▼
Set of inductive sets
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Set of natural numbers
▼
Set of integers
▼
Set of rademacher integers
▼
Rademacher integer
▼
Rademacher random integer
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Standard rademacher random integer
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Standard gaussian random real number
▼
Chi random unsigned real number
Definition D212
Chi-squared random unsigned real number
Formulation 0
Let
Z
1
,
Z
2
,
Z
3
,
⋯
∈
Gaussian
(
0
,
1
)
each be a
D211: Standard gaussian random real number
such that
(i)
Z
1
,
Z
2
,
Z
3
,
…
is an
D2713: Independent random collection
A
D3161: Random real number
X
∈
Random
(
R
)
is a
chi-squared random real number
with parameter
N
∈
{
1
,
2
,
3
,
…
}
if and only if
X
d
=
N
∑
n
=
1
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