Question: 8. (i) A necessary and sufficient condition for densities PII(x) to have monotone likelihood ratio in x, if the mixed second derivative a2IogplI(x)/ao ax exists,

8. (i) A necessary and sufficient condition for densities PII(x) to have monotone likelihood ratio in x, if the mixed second derivative a2IogplI(x)/ao ax exists, is that this derivative is 0 for all 0 and x. (ii) An equivalent condition is that a2PII(X) aplI(x) aplI(x) PII(X) aoax ao ax forallOandx .

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