=+19.7. The Neyman-Pearson lemma. Suppose

f, and f2 are rival densities and L( jli) is 0 or 1 as j = i or j # i, so that R,(8) is the probability of choosing the opposite density when

f, is the right one. Suppose of 8 that 82(w) = 1 if f2(w) > tff(w)

and 82(@) = 0 if fa(w) < tf,(w), where t > 0. Show that & is admissible: For any rule 8', forf, du < f82f, du implies f8, f2 du > f8, f2 du. Hint: ((82 - 82)