{
  "aliases": [
    "probability-generating-function",
    "pgf"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0Z8PSSAVBA"
    }
  ],
  "body": "\n## Summary\n\nThe probability-generating function of a random variable with values in $\\{0, 1, 2, \\dots\\}$ is the power series whose coefficients are the probabilities $P(X = k)$.\nThe node [[probability-generating function|0Z8PSSAVBA]] gives the precise definition.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "probability-generating-function",
      "pgf"
    ],
    "kind": "concept",
    "msc": [
      "60E05"
    ],
    "name": "Probability-generating function",
    "same_as": {
      "wikidata": "Q372071",
      "wikipedia": "Probability generating function"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Probability_generating_function"
      }
    ],
    "tag": "0EBCWQ8BVE"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0EBCWQ8BVE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0EBCWQ8BVE.md",
  "msc": [
    "60E05"
  ],
  "name": "Probability-generating function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0EB/0EBCWQ8BVE.md",
  "status": null,
  "tag": "0EBCWQ8BVE",
  "uri": "m2://0EBCWQ8BVE",
  "url": "https://math2.tamnd.com/wiki/probability-generating-function/",
  "writing": {
    "tag": "0EBCWQ8BVE",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}