Exchangeable random variables: Difference between revisions

Revision as of 04:47, 2 May 2009

Revision as of 04:48, 2 May 2009

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\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\quad{}}_\text{all ordered pairs} \\

& = n\sigma^2 + n(n-1)\operatorname{cov}(X_1,X_2),

\end{align}