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.

Bernoulli random variables and binomial random variables as sums of independent Bernoulli trials

Definition

For $p \in [0, 1]$ , a Bernoulli $(p)$ random variable takes the value $1$ with probability $p$ and $0$ with probability $1 - p$ .

For $n \in N$ , a binomial $(n, p)$ random variable is a sum $X = \sum_{i < n} X_{i}$ of $n$ mutually independent Bernoulli $(p)$ variables. When $n = 0$ , this is the constant zero random variable.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 36 results over 15 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

C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd ed., Section 5.1 (standard reference, not scraped)
H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Section 3.1.5 (standard reference, not scraped)