{
  "aliases": [
    "gaussian-distribution",
    "gaussian",
    "bell-curve"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "07RXBVTVZB"
    },
    {
      "field": "instance_of",
      "target": "0EYQ03XCR3"
    }
  ],
  "body": "\n## Summary\n\nThe normal distribution with mean $\\mu$ and variance $\\sigma^2$ is the continuous distribution on $\\mathbb{R}$ with the bell-shaped density $\\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-(x-\\mu)^2/(2\\sigma^2)}$.\nBy the central limit theorem, it is the approximate law of a sum of many small independent effects. The node [[normal distribution|07RXBVTVZB]] gives the precise definition.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "aliases": [
      "gaussian-distribution",
      "gaussian",
      "bell-curve"
    ],
    "kind": "concept",
    "msc": [
      "60E05"
    ],
    "name": "Normal distribution",
    "same_as": {
      "wikidata": "Q133871",
      "wikipedia": "Normal distribution"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Normal_distribution"
      }
    ],
    "tag": "05AQE0QR0D"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/05AQE0QR0D/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/05AQE0QR0D.md",
  "msc": [
    "60E05"
  ],
  "name": "Normal distribution",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/05A/05AQE0QR0D.md",
  "status": null,
  "tag": "05AQE0QR0D",
  "uri": "m2://05AQE0QR0D",
  "url": "https://math2.tamnd.com/wiki/normal-distribution/",
  "writing": {
    "tag": "05AQE0QR0D",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 1,
        "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
      }
    ]
  }
}