7. For a positive integer n, let t (n) = (2k, i), where i is the remainder when we divide n by 2*, the largest possible power of 2. For example, t(10) = (23, 2), T(12) = (23, 4), T(19) = (24, 3), and t(69) = (20, 5). In an experiment a point is selected at random from [0, 1]. For n 2 1, t(n) = (2k, i), let i+ 17 if the outcome is in Xn = 2 k ' 2 k 0 otherwise. Show that X,, converges to O in probability while it does not converge at any point, let alone almost sure convergence