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Competitive Stats
Q40Section B (Section B)40 of 60

Consistent estimators from the extremes of a shifted uniform

Let X1,X2,…,XnX_1,X_2,…,X_n be a random sample from U(θ,θ+1)U(\theta,\theta+1), where θ∈R\theta\in\mathbb R is the unknown parameter. Let U=max⁡{X1,X2,…,Xn}U=\max\{X_1,X_2,…,X_n\} and V=min⁡{X1,X2,…,Xn}V=\min\{X_1,X_2,…,X_n\}. Then which of the following statement(s) is (are) true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.