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Here is my math question. Is it possible to have random variables X, Y and Z for which simultaneously P(X > Y ) > 1/2,

Here is my math question.

Is it possible to have random variables X, Y and Z for which simultaneously P(X > Y ) > 1/2, P(Y > Z) > 1/2 and P(Z > X) > 1/2? Determine with proof the maximum possible value for min{P(X > Y ), P(Y > Z), P(Z > X)}.

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