A stick of length 1 is broken at a uniformly random point, yielding two pieces. Let X and Y be the lengths of the shorter and longer pieces, respectively, and let R = - X/Y be the ratio of the lengths X and Y. (a) Find the CDF and PDF of X. (b) Find the CDF and PDF of Y. (c) Find the CDF and PDF of R. (d) Find the expected value of X, Y, and R. (Hint: Let U denote the breaking point. Express X and Y each as a function of U. Express R as a function of X.)