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Competitive Stats
Q36Section B (Section B)36 of 60

Non-unique MLE for a uniform distribution of fixed width

Let X1,…,XnX_1,…,X_n (n>1n>1) be a random sample from a U(2θ−1,2θ+1)U(2\theta-1,2\theta+1) population, θ∈R\theta\in\mathbb R, and Y1=min⁡{X1,…,Xn}Y_1=\min\{X_1,…,X_n\}, Yn=max⁡{X1,…,Xn}Y_n=\max\{X_1,…,X_n\}. Which of the following statistics is (are) maximum likelihood estimator(s) of θ\theta?

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

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Select every correct option, then submit.