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It is absolutely wrong to say an exchangeable sequence is one in which future observations behave like past observations. In particular, that is not the case when they are negatively correlated. |
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In [[statistics]], an '''exchangeable sequence of random variables''' (also sometimes '''interchangeable''')<ref name="ChowTeicher"/> is a sequence ''X''<sub>1</sub>, ''X''<sub>2</sub>, ''X''<sub>3</sub>, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear is altered. Thus, for example the sequences
: <math> X_1, X_2, X_3, X_4, X_5, X_6 \quad \text{ and } \quad X_3, X_6, X_1, X_5, X_2, X_4 </math>
both have the same joint probability distribution.
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