Assuming that ZnZ, show that ZnZ. (Hint: You need to show that P(Zn x) ...

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Assuming that ZnZ, show that ZnZ. (Hint: You need to show that P(Zn ≤ x) → P(Z ≤ x) for all x where Fz(x) is continuous. If Fz(x) is continuous at x, then there is an interval (x - 6,x+8) in which Fz(x) is continuous. Further, Zn - Z| ≤e with high probability. Connect these pieces with suitable inequalities to get the result.) Assuming that ZnZ, show that ZnZ. (Hint: You need to show that P(Zn ≤ x) → P(Z ≤ x) for all x where Fz(x) is continuous. If Fz(x) is continuous at x, then there is an interval (x - 6,x+8) in which Fz(x) is continuous. Further, Zn - Z| ≤e with high probability. Connect these pieces with suitable inequalities to get the result.)

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