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Q117Section III (Statistics)117 of 190

Likelihood decreasing in θ\theta picks the smallest feasible value, X(n)/5X_{(n)}/5

Let X1,X2,…,XnX_1,X_2,\dots,X_n be a random sample from uniform (θ,5θ)(\theta,5\theta). Define X(1)=min⁡{X1,…,Xn}X_{(1)}=\min\{X_1,\dots,X_n\} and X(n)=max⁡{X1,X2,…,Xn}X_{(n)}=\max\{X_1,X_2,\dots,X_n\}. Maximum likelihood estimator of θ\theta is:

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