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Problem 3 (20p). Let (Xn), X be random variables taking values in R, and let f : R - R be continuous. (a) (5p) Show that if Xn -> X then fox fox. (b) (15p) Show that if Xn -> X then fo X -> fo X. Hint: recall from Lecture 26.1, Prop 1.2(b) that convergence in probability implies that a subsequence converges almost surely. Solution