Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = and E(Y ) =1/ where >

Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = β and E(Y ) =1/β where β > 0 as inExercise5.10andlet

(X1, Y1), ..., (Xn, Yn) be asamplefromthisdistribution.

a) Determineanasymptoticconfidenceintervalfor β based onthequadraticscore statistic usingthesample (X1, Y1), ..., (Xn, Yn).

b) Determineanasymptoticconfidenceintervalfor β from themomentestimator ˜ βn for β based on (X1, Y1), ..., (Xn, Yn) and thestatistic t(x, y) = x − y.

c) Makeasimulationstudytocomparethecoverageandlengthforthetwotypesof interval.