Exchangeable random variables: Difference between revisions

Revision as of 08:03, 13 December 2008

Revision as of 18:14, 13 December 2008

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== Properties ==

* [[Covariance]]: for a finite exchangeable sequence {&nbsp;''X''<mathsub>\{X_i\}_{''i=1,\ldots,n}''</mathsub>, &nbsp;}<mathsub>Cov (X_i,X_j) ''i''&nbsp;=const \ge -&nbsp;1/(n-1),&nbsp;2,&nbsp;3,&nbsp;...</mathsub>. Forof an infinite exchangeable sequence, <math>Cov (X_i,X_j) =const \ge 0</math>.length&nbsp;''n'':

:: <math> \operatorname{Cov} (X_i,X_j) = \text{constant} \ge \frac{-1}{n-1}.</math>

: "Constant" in this case means not depending on the values of the indices&nbsp;''i''&nbsp;and&nbsp;''j''.

* For an infinite exchangeable sequence,

:: <math> \operatorname{Cov} (X_i,X_j) = \text{constant} \ge 0.\,</math>

==See also==