Exchangeable events

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Let \xi=\{E_1,\ldots,E_n\} be a family of random events, and let X_1,\ldots,X_n be the indicator function for each of the events in ξ. Then ξ is said to be exchangeable if, for any permutation j_1,\ldots,j_n of the indexes 1,\ldots,n, the two random vectors (X_1,\ldots,X_n) and (X_{j_1},\ldots, X_{j_n}) have the same joint distribution.

With a more general view, a family of generic random variables (X_1,\ldots,X_n) is exchangeable if, for any permutation j_1\ldots,j_n of the indexes 1,\ldots,n, they have the same joint distribution.

Independent and identically random variables are exchangeable.

An interesting property of exchangeability is that the distribution function F_{X_1,\ldots,X_n}(x_1,\ldots,x_n) is symmetric in its arguments (x_1,\ldots,x_n).

[edit] See also

[edit] References

Spizzichino, Fabio Subjective probability models for lifetimes. Monographs on Statistics and Applied Probability, 91. Chapman & Hall/CRC, Boca Raton, FL, 2001. xx+248 pp. ISBN 1-58488-060-0

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