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Exercise 9. Let OCR and P = {/o(r): 0 O} be a family of functions on X CR satisfying fo(.) > 0 for all 0 O and EX. Assume that 202. log Jo(./') exists. (i) Show that P las monotone likelilood ratio in r is equivalent to one of the following conditions: logfo(.) > 0 for all x and 0; (b) fo(.1) 300, Jo(.')> 3 Jo(.) Jo(.) for all .r and 0. (ii) Let fo(1) be the Lebesgue density of the noncentral chi-square clistri- bution 10) with the noncentrality parameter () > 0. Show that the family P = {/o(.1): 0 >0} has monotone likelihood ratio in /