Problem 1. (12 pt) Let X be a continuous random variable with pdf f(x) and cdf F(x). For fixed values a and b with a < b, define the function 9(x) = { - f(x)/(F(b) F(a)) axb Prove that g(x) is a pdf. (Assume that F(b) F(a) > 0.) otherwise. In your solution, you should carefully state all the properties of a pdf.