Alphabeta MathHow 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.
Simple random sampling without replacement
Definition
Let be a finite population of size . For an integer with , simple random sampling without replacement (SRSWOR) of size is the sampling design whose support is and whose probability for every is Thus exactly distinct units are sampled and all -element subsets are equally likely.
Depends on
Used by
- Stratified sampling designs and the stratified total estimator Definition
- A three-unit SRSWOR variance calculation Example
- Census and singleton SRSWOR boundaries Example
- Zero pair support can prevent universal unbiased variance estimation Example
- Conditional CLT for a random subset of an IID finite population Lemma
- SRSWOR inclusion covariance and sample-mean variance Theorem
Dependency tree · two levels
10 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
- Shalabh, Sampling Theory, Chapter 2: Simple Random Sampling, PDF pp. 1–4 (standard reference, not scraped)