Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-13
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The indicator random variable of an event
Definition
For an event in a finite probability space, its indicator random variable is
Depends on
Used by
- SRSWOR inclusion probabilities, pairwise nonpositive indicator covariance, and the sample mean Example
- Indicators turn event probabilities, intersections, and finite counts into expectations and products Lemma
- A finite family of events is mutually independent exactly when its indicators are mutually independent Theorem
- Conditional hypergeometric moments for a logrank risk set Theorem
- The Horvitz–Thompson total and mean are design-unbiased under positive inclusion probabilities Theorem
Dependency tree · two levels
5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- J. Matousek and J. Vondrak, The Probabilistic Method, Definition 3.1.2 (standard reference, not scraped)
- M. Bucic, Probabilistic Method, Section 2.1 (standard reference, not scraped)