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If Yₙ is 1 or 0 depending on whether the nth ball drawn in a Polya urn scheme is red or not, then the variables Y₁, Y₂,… are exchangeable. It is shown for a generalized class of urn models that no other scheme gives rise to exchangeable variables unless the Yₙ are either independent and identically distributed, or deterministic (that is, all of the Yₙ's have the same value with probability 1).
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Hill et al. (1987) studied this question.
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