3. (20 points) (Convergence in Probability) Let X1, X2, ... be independent random variables that are uniformly distributed over [-1, 1]. Show that the sequence Y1, Y2, ... converges in probability to some limit, and identify the limit for each of the following cases: (a) (5 points) Yn = Xn (b) (5 points) Ym = (X, )" (c) (5 points) Yn = X1 . X2 . . . Xn (d) (5 points) Yn = max{ X1, . .., Xn}