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Corr(X,Y) = 0.9 and Corr(Y,Z) = 0.8. What are the minimum and maximum possible values of Corr(X,Z)?

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Corr(X, Y) = 0.9 and Corr(X, Z) = 0.9. What range of values can Corr(Y, Z) take?There are three random variables A, B and C. corr(A,B) = 0.6 and corr(A,C) = 0.8. What range of values can corr(B,C) take?If a + b + c + d = 63, what's the maximum value of a * b + b * c + c * d?

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