Derive formulas for the c.d.f. FY (y), and the p.d.f. fY (y), of a transformation Y = g(X) of a random quantity X, in terms of its c.d.f. FX(x), and p.d.f. fX(x), in the case when the trans- forming function y = g(x) is monotonically decreasing. Follow the line of reasoning used to derive the analogous formulas (3.1.11)-(3.1.12) for monotonically increasing transformations. How would you extend these formulas to transformations that are monotonically increasing on some intervals and decreasing on their complement?