A finite sequence of random variables is exchangeable if the distribution of the sequence is unchanged for every permutation of the indices. Infinite sequence $\{ X_i \} _{i \in \mathbb{N}}$ of random variables is exchangeable, if the finite sequences $X_1,...,X_n$ are exchangeable for every natural number $n$. If the random variables are exchangeable, then they are identically distributed. In general the opposite does not hold. It holds if we have an infinite sequence of exchangeable random variables. It is obviously true in the case that identically distributed random variables have independent property as well. De Finetti's theorem says that an exchangeable infinite sequence of Bernoulli random variables is a ‘mixture' of independent sequences conditional on measure $\mu$ on $[0,1]$.
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