Question: 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 R.
(b) Find the expected value of R (if it exists).
(c) Find the expected value of 1/R (if it exists).