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* Suppose an urn contains ''n'' red and ''m'' blue marbles. Suppose marbles are drawn without replacement until the urn is empty. Let ''X''<sub>''i''</sub> be the indicator random variable of the event that the ''i''th marble drawn is red. Then {''X''<sub>''i''</sub>}<sub>''i''=1,...''n''</sub> is an exchangeable sequence. This sequence cannot be extended to any longer exchangeable sequence.
== Applications ==
;[[von Neumann extractor]]:
The [[von Neumann extractor]] is a [[randomness extractor]] that depends on exchangeability: it gives a method to take an exchangeable sequence of 0s and 1s ([[Bernoulli trials]]), with some probability ''p'' of 0 and <math>q=1-p</math> of 1, and produce a (shorter) exchangeable sequence of 0s and 1s with probability 1/2.
Partition the sequence into non-overlapping pairs: if the two elements of the pair are equal (00 or 11), discard it; if the two elements of the pair are unequal (01 or 10), keep the first. This yields a sequence of Bernoulli trials with <math>p=1/2,</math> as, by exchangeability, the odds of a given pair being 01 or 10 are equal.
== Properties ==
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