Question: Let p_0(x) and p_1(x) be continuous densities with continuous likelihood ratio L(x) := p_1(x)/p_0(x). Show that for any t > 0, P_0{L(X) t} P_1{L(X) t}.

Let p_0(x) and p_1(x) be continuous densities with continuous likelihood ratio L(x) := p_1(x)/p_0(x). Show that for any t > 0, P_0{L(X) t} P_1{L(X) t}. Explain why this implies that the power function is monotone

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