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Expositio paper exp-20261012-da6e1e

Central Limit Theorem

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In this paper, we will prove a few different versions of the Central Limit Theorem: first, a weak one, then the Lindeberg and Liapunov Central Limit Theorems. Additionally, we will show the Central Limit Theorem in action and explain why it is one of the mo…

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exp-20261012-da6e1ev1 Latest public version Public since October 12, 2026 Submitted October 12, 2026 0 saves
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Justin Cheong (Mountain View High School, Mountain View, CA)

Abstract

In this paper, we will prove a few different versions of the Central Limit Theorem: first, a weak one, then the Lindeberg and Liapunov Central Limit Theorems. Additionally, we will show the Central Limit Theorem in action and explain why it is one of the most useful theorems in all of statistics.

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Mathematics
Main field
Probability theory and stochastic processes Limit theorems in probability theory Central limit and other weak theorems
Mathematics
Statistics Statistical distribution theory Asymptotic distribution theory in statistics

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exp-20261012-da6e1ev1

Central Limit Theorem

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Uploaded Oct 12, 2026 2056317 bytes Selected Latest
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