Let (v) be the probability space consisting of Lebesgue measure on the Borel subsets of [0, 1]. Each in [0, 1] may be written in binary expansion as o-X,X, - where X-X)-0 or 1 and this expansion is unique except for a set of as of the form w/2" which is countable and hence has probability (Lebesgue measure) zero. For definiteness regarding such as, only the expansion consisting of infinitely many ones will be used. Show that for alle 21, X) 11e and that [X] is a sequence of independent rva. Describe the rvs Y, where or , and is an integer>2