(a) Show that if a family of pdfs {f(x|): } has an MLR, then the...

Question:

(a) Show that if a family of pdfs {f(x|θ): θ ∈ ⊝} has an MLR, then the corresponding family of cdfs is stochastically increasing in 6. (See the Miscellanea section.)
(b) Show that the converse of part (a) is false; that is, give an example of a family of cdfs that is stochastically increasing in 9 for which the corresponding family of pdfs does not have an MLR.