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Suppose $X_1,\ldots,X_n$ are a random sample of $U(-\theta,\theta)$ with $\theta>0$. How can find $$ E\left(|X_1|\ \big|\max |X_i| \right) $$ that $1\leq i\leq n$?

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    Interestingly, if $\theta$ is unknown, then $E\left(|X_1|\ \big|\max |X_i| \right)=E(Y_1\mid \max Y_i)$ is the UMVUE of $\frac{\theta}{2}$ where $Y_i=|X_i|\sim U(0,\theta)$ as mentioned in an answer below.2018-08-13

2 Answers 2