De Finetti's Theorem states that an infinite sequence of exchangeable random variables, meaning its joint distribution is unchanged by any reordering of finitely many terms, can always be represented as a mixture of sequences of independent and identically distributed random variables, conditioned on an underlying random parameter. Named for Bruno de Finetti, it is a foundational result of probability theory providing a rigorous basis for the Bayesian interpretation of exchangeable data as arising from an unknown but fixed underlying probability.
Facts
StatementDe Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a mixture of the probability distributions of independent and identically distributed sequences of Bernoulli random variables. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source De Finetti's theorem, Wikipedia
Sources
1. De Finetti's theorem, Wikipedia
Lead section
De Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a mixture of the probability distributions of independent and identically distributed sequences of Bernoulli random variables.
In Branch: Probability and Statistics, Lead sentence
In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some l
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