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(#6.11). Let X be an observation with a probability density in the family P = {fo : 0 O}, where o C R is the possible values of the parameter 2. (i) Show that P has monotone likelihood ratio in X when = R and fo is the Lebesgue density of the double exponential distribution with location parameter 0 and a known scale parameter c. (ii) Show that P has monotone likelihood ratio in X when 0 = R and fo is the Lebesgue density of the exponential distribution on the interval (0,00) with a known scale parameter c. (iii) Show that P has monotone likelihood ratio in X when = R and fo is the Lebesgue density of the logistic distribution with location parameter 0 and a known scale parameter c. (iv) Show that P has monotone likelihood ratio in X when = R and fe is the Lebesgue density of the uniform distribution on (0,0 + 1). (v) Show that P has monotone likelihood ratio in X when o = {1, 2,...} and fo(x) = (*)(n-3)/(%) when x is an integer between r 0 and min{r,0}, where r and N are known integers. (vi) Show that P does not have monotone likelihood ratio in X when =R and fo is the Lebesgue density of the Cauchy distribution with location parameter 0 and a known scale parameter c