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Competitive Stats
Q16Section I (Objective (Q1–Q80))16 of 80

Statistical Inference — MLE of theta for U(0,5 theta)

Let X1,X2,X3,...,XnX_1, X_2, X_3, ..., X_n be a random sample from U(0,5θ)U(0,5\theta). Define X(1)=min⁡(X1,...,Xn)X_{(1)}=\min(X_1,...,X_n) and X(n)=max⁡(X1,...,Xn)X_{(n)}=\max(X_1,...,X_n). Then the maximum likelihood estimator of θ\theta is

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