Given a pair of random variables X and Y having the variances 21 and 22 and the correlation coefficient , use Theorem 4.14 to express

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.