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Let X1,…, Xn be a sample of iid U[?, 1] random variables with Θ = (−∞,...

Let X1,…, Xn be a sample of iid U[?, 1] random variables with Θ = (−∞, 1].

a) Show that T = (1−X(1) )/(1−?) is a pivotal quantity.

b) Determine an exact (1 − ?) × 100% confidence interval for ? based on T.

c) Determine an exact (1 − ?) × 100% upper-bound confidence interval for ? based on T.

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