We already computed Cov(X, Y ) = −13/5000 in Section 10.2. Hence, by the linearity-of-covariance rule Cov(−2X + 7, 5Y − 3) = (−2)·5·(−13/5000) = 13/500.
2. From Quick exercise 10.4 we have Cov(−2X + 7, 5Y − 3) = 13/500. Since Var(X) = 989/2500 and Var(Y ) = 791/10 000, by definition of the correlation coefficient and the rule for variances,
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