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Let X1, … , X5 denote a random sample of size 5 from the density f(x; θ)
(a) Determine the confidence coefficient of the confidence interval (Y1, Y5).
(b) Find a confidence interval for 0 that has the same confidence coefficient as in part (a) using the pivotal quantity (Y1 + Y5)/2 – θ.
(c) Compare the expected lengths of the confidence intervals of parts (a) and (b).