The Weibulldistribution with shapeparameter > 0 has density function f(x) = x1ex with respecttostandardLebesguemeasureon R+. TheWeibulldistributionis,for

The Weibulldistribution with shapeparameter α > 0 has density function fα(x) = αxα−1e−xα

with respecttostandardLebesguemeasureon R+. TheWeibulldistributionis,for example,muchusedinReliabilityTheoryasadistributionofthetimetofailureofa component inacomplexsystem.Assumethat X followssuchaWeibulldistribution.

Construct a95%two-sidedconfidenceinterval C(X) for α based ontheuniversal pivot.