{"id": "card_v_e25edb860b45", "kind": "verified", "title": "E[Binom(10, ½)] = n·p = 5 · P(X=2) = C(10,2)·½¹⁰ = 45/1024 ≈ 0.04395", "body": "Verdict: HOLDS.\n• probability.binomial_mean: E[Binom(10,0.5)] = 5.0\n• probability.binomial: P(X=2 | n=10, p=0.5) = 0.0439453\nSealed and independently re-checkable: https://narrowhighway.com/s/e50261aa12a5d659f1567480f4802f5156bdb9e44fbb190a17e3f0d8e557d34f", "source": {"label": "Verified by the engine — probability", "url": "https://narrowhighway.com/s/e50261aa12a5d659f1567480f4802f5156bdb9e44fbb190a17e3f0d8e557d34f", "ref": "", "domain": "probability", "authority_tier": "engine"}, "shelf": "probability", "box": "verified", "bands": ["verified", "probability", "HOLDS"], "connections": [{"to_card_id": "card_k_spine_created_order", "relationship": "part_of", "evidence": "a verified seed of the created order (probability)"}, {"to_card_id": "card_works_probability", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (probability)."}, {"to_card_id": "card_works_bayes", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (probability)."}], "author": "engine", "created_at": 1784892567.9337015, "updated_at": 1784892567.9337022, "visibility": "public", "lifecycle_stage": "public", "volatility": "durable", "surface": "secular", "generated": false, "presentation": {"glyph": "•", "kind_label": "verified", "by": "Verified by the engine — probability", "authority": "engine", "posted": "1 month ago", "standing": "", "link": {"url": "https://narrowhighway.com/s/e50261aa12a5d659f1567480f4802f5156bdb9e44fbb190a17e3f0d8e557d34f", "host": "narrowhighway.com", "provider": "", "titled": "E[Binom(10, ½)] = n·p = 5 · P(X=2) = C(10,2)·½¹⁰ = 45/1024 ≈ 0.04395", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_k_spine_created_order", "title": "The created order — the science of the floor", "relationship": "part of", "why": "a verified seed of the created order (probability)", "href": "/card/card_k_spine_created_order", "resolved": true}, {"id": "card_works_probability", "title": "Ten fair coins: the average and a particular outcome", "relationship": "demonstrates", "why": "A worked demonstration in the same field (probability).", "href": "/card/card_works_probability", "resolved": true}, {"id": "card_works_bayes", "title": "The base rate a doctor must not forget", "relationship": "demonstrates", "why": "A worked demonstration in the same field (probability).", "href": "/card/card_works_bayes", "resolved": true}]}