(Answered) Let x1 xnnbspn gt 1 be iid from the exponential

Statistics

Let X₁, ..., X_n (n > 1) be i.i.d. from the exponential distribution E(θ, θ), where θ > 0 is unknown.

(a) Show that both X/Θ and X₍₁₎/θ are pivotal quantities, where X is the sample mean and X₍₁₎ is the smallest order statistic.

(b) Obtain confidence intervals (with confidence coefficient 1 - α) for θ based on the two pivotal quantities in (a).

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