{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/read-expected-value-as-a-weighted-average-of-possibilities",
  "id": "MHC-D-RESEARCH-0258",
  "version": "0.1.0",
  "title": "Read expected value as a weighted average of possibilities",
  "summary": "An expected outcome need not be an outcome that ever occurs once.",
  "kind": "concept",
  "body": "Multiply each possible outcome by its probability and add the products. Then inspect the actual possibilities as well as their average. A low expected cost can coexist with a rare loss that is unacceptable to the person bearing it.",
  "limits": [
    "Expected value alone does not determine a sensible personal or safety-critical decision."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-411C025BAB45499C"
  ],
  "evidence": [
    {
      "claim": "A discrete expected value is the sum of possible outcomes weighted by their probabilities, and it need not be a possible single outcome.",
      "source_id": "RS-411C025BAB45499C",
      "role": "supports",
      "note": "An expectation does not describe tail risk, affordability of a loss or the reliability of the probabilities.",
      "locator": "Expected-value definition"
    }
  ],
  "use_when": [
    "A model gives one expected result for a decision with several possible outcomes."
  ],
  "avoid_when": [
    "Expected value alone does not determine a sensible personal or safety-critical decision."
  ],
  "example": "An invented process with a 90% chance of zero rework and a 10% chance of 100 minutes has expected rework of 10 minutes, though neither run takes exactly 10.",
  "check": "The expectation is accompanied by its assumptions and important tail outcomes.",
  "sources": [
    {
      "id": "RS-411C025BAB45499C",
      "title": "Introductory Statistics 2e, 4.2: Mean or Expected Value and Standard Deviation",
      "url": "https://openstax.org/books/introductory-statistics-2e/pages/4-2-mean-or-expected-value-and-standard-deviation"
    }
  ],
  "relations": [
    {
      "from": "MHC-D-RESEARCH-0258",
      "to": "MHC-D-RESEARCH-0250",
      "type": "useful_with",
      "url": "/knowledge/put-variation-beside-the-average"
    }
  ],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}