1.2 Exchangeability

1.2.1 Distributional Symmetry

Definition 1.11 Exchangeable

• $X_{1}, \ldots, X_{n}$,
  • random quantities

$X_{1}, \ldots, X_{n}$ is said to be exchangeable if

\[\sigma \in \mathfrak{S}_{n}, \ (X_{\sigma(1)}, \ldots, X_{\sigma(n)}) \sim (X_{1}, \ldots, X_{n}) .\]

• $(X_{i})_{i \in \mathbb{N}}$,
  • random quantities

$(X_{i})$ is said to be exchangeable if for every finite sequence are exchangeable.

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