Central Limit Theorem (modern form)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:statistical_theorem
gptkbp:appliesTo	random variables with finite mean and variance
gptkbp:category	gptkb:statistical_analysis probability theorems
gptkbp:describes	distribution of sum of independent random variables
gptkbp:form	(X₁ + X₂ + ... + Xₙ - nμ)/(σ√n) → N(0,1) as n → ∞
gptkbp:formedBy	early 20th century
gptkbp:generalizes	gptkb:Berry–Esseen_theorem gptkb:Lindeberg–Feller_theorem Lyapunov central limit theorem
gptkbp:implies	sample mean approximates normal distribution as sample size increases
gptkbp:provenBy	gptkb:Pierre-Simon_Laplace gptkb:Jarl_Waldemar_Lindeberg gptkb:Aleksandr_Lyapunov gptkb:Andrey_Kolmogorov
gptkbp:relatedTo	gptkb:normal_distribution gptkb:law_of_large_numbers
gptkbp:requires	finite variance identical distribution (in classical form) independence of random variables
gptkbp:state	sum of large number of independent, identically distributed random variables tends toward normal distribution
gptkbp:usedIn	gptkb:machine_learning gptkb:probability_theory data science statistics
gptkbp:bfsParent	gptkb:Central_Limit_Theorem_(early_form)
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	Central Limit Theorem (modern form)