{
  "id": "2106.00871",
  "version": "v1",
  "published": "2021-06-02T00:43:38.000Z",
  "updated": "2021-06-02T00:43:38.000Z",
  "title": "A Short and Elementary Proof of the Central Limit Theorem by Individual Swapping",
  "authors": [
    "Calvin Wooyoung Chin"
  ],
  "comment": "6 pages, to be published in the American Mathematical Monthly",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of swapping a term for a normal random variable in turn. The modifications needed to prove the stronger Lindeberg-Feller central limit theorem are addressed at the end.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T00:43:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "elementary proof",
      "individual swapping",
      "stronger lindeberg-feller central limit theorem",
      "linear operators",
      "lindebergs trick"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}