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Could you please guide on how to approach this confidence interval review problem? Let U1, U2,...

Could you please guide on how to approach this confidence interval review problem? Let U1, U2, · · · , Un be i.i.d observations from Uniform(0, θ), where θ > 0 is unknown. Suppose U(1) = min{U1, U2, · · · , Un} and U(n) = max{U1, U2, · · · , Un}.

Show that for any α ∈ (0, 1),

(U(1), α-1/nU(n))

is a (1 − α) level confidence interval for θ.

Math   Statistics-And-Probability   
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