b. For n ≥ 2, let X₁, X2,..., Xn be i.i.d. samples from the the uniform distribution U(0,0 + 1) where is some real number. Let X(1) ≤X(2) ≤ ≤ X(n) 12- be the order statistics of the sample. [i.] Show that (X(1), X(n)) is a sufficient statistic for 0. [ii.] Find an and b(0) such that an (b(0) — X(n)) → W in distribution, where W has an exponential distribution with density f(w) = e, for w> 0 and 0 elsewhere.

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