Exercise3.11 Let t1, ..., tn exp(). InExample3.6,weconstructed95%confidenceintervalsfor , = Et = 1/ and p =

Exercise3.11 Let t1, ..., tn ∼ exp(θ). InExample3.6,weconstructed95%confidenceintervalsfor

θ, μ = Et = 1/θ and p = P(t > 5) = e−5θ based onthepivot2θ Σni

=1 ti ∼ χ2 2n. Showthatanother pivotis θtmin ∼ exp(n). Useittoconstruct95%confidenceintervalsfor θ, μ, and p, andcompare them withthosefromExample3.6forthesamedata.

Exercise3.12 If Lα/2 and Uα/2 are thelowerandupper (1−α/2)100% confidencebounds,then

(Lα/2 , Uα/2) is a (1−α)100%-levelconfidenceintervalfor θ.