The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

with replacement, without replacement concept

DefinitionDrawing rows with replacement lets a row appear more than once, as the bootstrap does, and drawing without replacement lets each appear at most once. Primer S section S.11. Also with replacement, without replacement.
ExampleA bootstrap draw of 2, 4, 4, 4, 5, 5, 7, 9 might be 4, 9, 2, 5, 4, 4, 7, 9, with the 9 twice and one 5 left out.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id replacement, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

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Conditions

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Ledger

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First stated

Primer S section S.11 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.

Measurements

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Failures and corrections

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Invariance envelope

none declared

Machine checked

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Used in

Data Mining as Observation primer S, chapters 0.

Related

bootstrap; sampling; percentile interval.

See also

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Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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