Problem 6.LetXhave densityfwitha < < b. Suppose we are interested in testingH0:0versusH1: < 0, where0belongs to the interval (a, b). Suppose the test(X) is NP(f2, f1) foreverya<1<2

(1)Show that the power functionof the test(X) is nonincreasing. Recallis defined by() =E((X)), a < < b.

(2)Find the size of the test(X).

(3)Suppose(X) is another test with satisfiesE0((X))E0((X)). Show thatE((X))() holds for every < 0.