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* [[Covariance]]: for a finite exchangeable sequence { ''X''<sub>''i''</sub> }<sub>''i'' = 1, 2, 3, ...</sub> of length ''n'':
:: <math> \operatorname{
: where ''σ''<sup> 2</sup> = var(''X''<sub>1</sub>).
: "Constant" in this case means not depending on the values of the indices ''i'' and ''j'' as long as ''i'' ≠ ''j''.
: This may be seen as follows:
:: <math>
\begin{align}
0 & \le \operatorname{var}(X_1 + \cdots + X_n) = \operatorname{var}(X_1) + \cdots + \operatorname{var}(X_n) + \underbrace{\operatorname{cov}(X_1,X_2) + \cdots}_\text{all ordered pairs} \\
& = n\sigma^2 + n(n-1)\operatorname{cov}(X_1,X_2),
\end{align}
</math>
: and then solve the inequality for the covariance. Equality is achieved in a simple urn model: An urn contains 1 red marble and ''n'' − 1 green marbles, and these are sampled without replacement until the urn is empty. Let ''X''<sub>''i''</sub> = 1 if the red marble is drawn on the ''i''th trial and 0 otherwise.
the case in which ''X''<sub>''i''</sub> is
* For an infinite exchangeable sequence,
:: <math> \operatorname{
==See also==
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