Question: 18. Let X and Y be two randomly selected numbers from the set of positive integers {1, 2, . . . , n}. Prove that

18. Let X and Y be two randomly selected numbers from the set of positive integers {1, 2, . . . , n}. Prove that ρ(X, Y ) = 1 if and only if X = Y with probability 1. Hint: First prove that E 4 (X − Y )2 5 = 0; then use Exercise 17.

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