This will establish the converse is false, i.e., X, => X does not imply X, -p X. Suppose X and a sequence of rvs X1, X2,... are iid Bernoulli( ), i.e., P(X, = 1) = =1 -P(Xi = 0). (a) Establish X, = X. (This is a trivial result, so make sure to indicate why this is obvious.) (b) Show (Xn - X| ~ Bernoulli(;). (Hint: Compute the pmf for [X, - X|.) (c) For E E (0, 1), find lim P(|Xn - X| > =). n-+00 (d) By part (c), conclude Xn Ap X