{
  "aliases": [
    "probability-calculus"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nProbability theory is the branch of mathematics that studies chance in a precise way.\nIt models a random experiment by a [[probability space|0ZYBZ34RT2]]: a sample space, a family of events and a probability measure that obeys the [[probability axioms|0DAX8PMAJ4]].\nIts main objects are events, random variables, their distributions and their expected values.\nIts main results include limit theorems, such as the law of large numbers and the central limit theorem.\n\n## Remarks\n\nThe modern axioms are due to Andrey Kolmogorov, who based them on measure theory in 1933.\nStatistics uses probability theory to draw conclusions from data.\n\n## Explanations\n\n### L1 human\n\nProbability theory gives numbers to uncertain things, such as the chance of rain or the chance of a six on a die.\nThe rules for these numbers are few and simple, but they give strong results.\nFor example, the average of many fair coin tosses is close to one half.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "probability-calculus"
    ],
    "kind": "concept",
    "msc": [
      "60A05"
    ],
    "name": "Probability theory",
    "same_as": {
      "wikidata": "Q5862903",
      "wikipedia": "Probability theory"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Probability_theory"
      }
    ],
    "tag": "0RWE7CPJ32"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0RWE7CPJ32/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0RWE7CPJ32.md",
  "msc": [
    "60A05"
  ],
  "name": "Probability theory",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0RW/0RWE7CPJ32.md",
  "status": null,
  "tag": "0RWE7CPJ32",
  "uri": "m2://0RWE7CPJ32",
  "url": "https://math2.tamnd.com/wiki/probability-theory/",
  "writing": {
    "tag": "0RWE7CPJ32",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}