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Determining the standard normal distribution

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Let X1, ..., Xn be i.i.d. with a Lebesgue p.d.f. f(x - µ), where f is known and µ is unknown.

(a) If f is the p.d.f. of the standard normal distribution, show that the confidence interval [X - c1, X + c1] is better than [X1 - c2, X1 +c2] in terms of their lengths, where ci's are chosen so that these confidence intervals have confidence coefficient 1 - α.

(b) If f is the p.d.f. of the Cauchy distribution C(0, 1), show that the two confidence intervals in (a) have the same length.

Reference no: EM131852139

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