# Central limit theorem for finite-variance IID sequences

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Central limit theorem for finite-variance IID sequences](https://ocme.evemisslab.com/en/atlas/atlas-central-limit-theorem-finite-variance-iid/)

An infinite IID sequence with common finite positive variance has centered sums scaled by sigma*sqrt(n) converging in distribution to the standard normal law.

atlas-central-limit-theorem-finite-variance-iid · canonical_mko

[Central limit theorem for finite-variance IID sequences](https://ocme.evemisslab.com/en/mko/mko-central-limit-theorem-finite-variance-iid/)

## Prerequisite nodes


- [Independent identically distributed sequence](https://ocme.evemisslab.com/en/atlas/atlas-iid-sequence/)
- [Convergence in distribution](https://ocme.evemisslab.com/en/atlas/atlas-convergence-in-distribution/)
- [Expectation in finite models](https://ocme.evemisslab.com/en/atlas/atlas-expectation/)
- [Variance in finite probability models](https://ocme.evemisslab.com/en/atlas/atlas-variance/)
- [Standard normal distribution](https://ocme.evemisslab.com/en/atlas/atlas-standard-normal-distribution/)
- [Sigma-algebras and measure spaces](https://ocme.evemisslab.com/en/atlas/atlas-sigma-algebra-measure-space/)
- [Binomial theorem](https://ocme.evemisslab.com/en/atlas/atlas-binomial-theorem/)