1. By the time you reach Math 183, you know how to find the distance between two numbers (16 - al), between two points (V(xA -XB)2 + (yA - yB)2), and between other mathematical objects. Is it possible to define a distance between two pdfs? One approach is to set the distance between pdfs f(x) and g(x), denoted d(f, g), as V2(1 - p) where P = Vf(x) . g(x) da a. [2 points] Let's see if this definition makes any sense. Show d( f, f ) = 0, as we might hope. b. [3 points] Let X1 ~ Exp() = a) have pdf fi(x) and X2 ~ Exp() = 3) have pdf f2(x). Find a simplified expression for d( f1, f2). As always, use beautiful notation when integrating. c. [2 points] What is the biggest value d(f, g) could have in general? After explaining why this is the biggest value, dream up two specific pdfs that have this largest possible distance