(10 points) A few unrelated questions. Justify each of your answers, this means prove or give a counterexample for each of the questions. a) Let X be a continuous random variable with distribution Fx. Does there exist a random Y such that its distribution Fy satisfies Fy(x) = 2Fx(x)? b) Let X ~ N(0, 1) and Y ~ W(0, 1) be independent. Then X2 + Y is an exponential random variable. c) Let X and Y be two jointly continuous random variables with joint distribution Fxy and marginal distributions Fx and Fy, respectively. Suppose that Fxy(a, b) = Fx (a) FY(b) for every a, be Z. Does this imply that X and Y are independent