Let X > 0 denote a random variable with p.d.f. fX(x) and c.d.f. FX(x). Assume FX(·) is monotone increasing, and let Y = FX(X). That is, Y is a random variable that takes the value FX(x) when X = x. Find fY (y).
1) fY (y) = 1, 0 < y < 1
2) fY (y) = d dx FX(x) = f(x)
3) fY (y) = fX(F -1 X (y))
4) fY (y) ∠ y(1 - y)
5) none of these
