Elementary Proofs of the Main Limit Theorems of Probability
Nicholas Pippenger
TL;DR
This paper provides straightforward, elementary proofs of the Weak Law of Large Numbers and the Central Limit Theorem for i.i.d. random variables, using only basic calculus and probability concepts.
Contribution
It introduces simple, minimal-hypothesis proofs of key probability theorems, making them more accessible and easier to understand.
Findings
Proofs require only elementary calculus and basic probability notions
The approach simplifies understanding of fundamental limit theorems
Results hold under minimal assumptions for i.i.d. variables
Abstract
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most basic notions of probability, expectations, and distribution functions
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsProbability and Statistical Research · Bayesian Modeling and Causal Inference