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

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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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