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Three variables have pairwise correlations 0.5, 0.3 and -0.3. A fourth variable is added. What is the largest possible sum of its correlations with the three?

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Three random variables have correlations cor(x1,x2) = 0.5, cor(x1,x3) = 0.3 and cor(x2,x3) = -0.3. A fourth variable x4 is added. What is the maximum possible value of cor(x1,x4) + cor(x2,x4) + cor(x3,x4)?

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