Exchangeable random variables: Difference between revisions

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Properties: this is wrong without the sigma squared
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* [[Covariance]]: for a finite exchangeable sequence {&nbsp;''X''<sub>''i''</sub>&nbsp;}<sub>''i''&nbsp;=&nbsp;1,&nbsp;2,&nbsp;3,&nbsp;...</sub> of length&nbsp;''n'':
 
:: <math> \operatorname{Cov} (X_i,X_j) = \text{constant} \ge \frac{-1\sigma^2}{n-1}.,\quad\text{for }i \ne j,</math>
 
: where ''&sigma;''<sup>&nbsp;2</sup>&nbsp;=&nbsp;var(''X''<sub>1</sub>).
 
: "Constant" in this case means not depending on the values of the indices&nbsp;''i''&nbsp;and&nbsp;''j'' as long as ''i''&nbsp;≠&nbsp;''j''.