A stick of length I 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 = XI Y be the ratio of the lengths of)! and Y. (a) Use simulations in R (the statistical programming language) I. gain some understanding about line distribution of the random variable R. Numerically estimate the expected value of R and UK (b) Find the GDP and PDF of R. (c) Find the expected value of R (if it exists). (d) Find the expected value of 1/]? (if it exists)