▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Measurable space
▾ Measure space
▾ Probability space
▾ Independent event collection
▾ Independent collection of event collections
▾ Independent collection of sigma-algebras
▾ Independent random collection
I.I.D. random collection
Formulation 0
A D1721: Random collection $X : J \to \text{Random}(\Omega \to \Xi)$ is independent and identically distributed if and only if
(1) $X$ is an D2713: Independent random collection
(2) $X$ is an D3357: Identically distributed random collection
Child definitions
» D5289: Strong white noise random real collection
Results
» R3598: Wald's first equation under independence
» R2368: I.I.D. real strong law of large numbers with the identity index sequence
» R2410: I.I.D. real weak law of large numbers under finite second absolute moments
» R4684: I.I.D. weak law of large numbers for random real numbers
» R4685: I.I.D. weak law of large numbers for random real numbers of finite first absolute moments
» R5404: I.I.D. real central limit theorem
» R5405: Standard I.I.D. real central limit theorem
» R5408: I.I.D. real strong law of large numbers
» R5412:
» R5413:
» R5416:
» R5418: Counterexample to Wald's first equation when independence not satisfied
» R5419: Wald's first equation
» R5423: Wald's second equation under independence
» R5424: