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Q19Section A (Section A)19 of 60

MLE for a shifted uniform family

Let X1,X2,…,XnX_{1},X_{2},…,X_{n} (n≥2)(n\ge 2) be a random sample from U(θ−5,θ+5)U(\theta-5,\theta+5), where θ∈(0,∞)\theta\in(0,\infty) is unknown. Let T=max⁡{X1,X2,…,Xn}T=\max\{X_{1},X_{2},…,X_{n}\} and U=min⁡{X1,X2,…,Xn}U=\min\{X_{1},X_{2},…,X_{n}\}. Then, which of the following statements is TRUE?

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