(a) Is it possible for a continuous function f(x) to satisfy all of the following properties? (i) f(x)≥0 for all x in some interval (a, b), and 0 elsewhere (ii) f(x)dx=1 (iii) x f(x)dx=2 (iv) x²f(x)dx=3 If so, provide an example; if not, provide a formal mathematical proof. Show all work. (10 pts) (b) Answer part (a) if the last property were replaced by fox² f(x)dx=4. In this case, what can be said about the random variable X, and why? Show all work. (5 pts)