DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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 moment generating function $M_{X} (t) = E [e^{t X}]$ on a finite probability space

Definition

For a finite real random variable $X$ , its moment generating function is the everywhere-defined function $M_{X} (t) : = E [\exp (t X)], t \in R .$ Finiteness of the outcome space makes this a finite sum, so no convergence hypothesis is needed.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 49 results over 11 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

Y. Zhao, MIT 18.218 Probabilistic Method in Combinatorics, Section 4.1 (standard reference, not scraped)

The moment generating function MX(t)=E[etX]MX​(t)=E[etX] on a finite probability space