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Assume X = $(X_1, ..., X_n)$ ~ $U(\theta, 2\theta)$, where $\theta \in \Bbb{R}^+$.

How does one calculate the conditional expectation of $E[X_1|X_{(1)},X_{(n)}]$, where $X_{(1)}$ and $X_{(n)}$ are the smallest and largest order statistics respectively?

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closed as off-topic by Davide Giraudo, rschwieb, callculus, Adrian Keister, Brevan Ellefsen Apr 16 at 19:27

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