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Q154Section III (Statistics)154 of 190

At n=2n=2 the sample mean and the midrange are literally the same statistic

Let X1,X2,…,XnX_1,X_2,\dots,X_n be iid U(0,θ)U(0,\theta). Define T1=XˉT_1=\bar X and T2=(X(1)+X(n))/2T_2=(X_{(1)}+X_{(n)})/2, where X(1)=min⁡(X1,…,Xn), X(n)=max⁡(X1,…,Xn)X_{(1)}=\min(X_1,\dots,X_n),\ X_{(n)}=\max(X_1,\dots,X_n). Then:

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