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Given a pair of random variables X and Y having

Given a pair of random variables X and Y having the variances σ21 and σ22 and the correlation coefficient ρ, use Theorem 4.14 to express var(X/s1 + Y/s2) and var(X/s1 – Y/s2) in terms of σ1, σ2, and ρ. Then, making use of the fact that variances cannot be negative, show that –1 ≤ ρ ≤ + 1.

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