a. Use the rules of expected value to show that Cov(aX + b, cY + d) 5

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a. Use the rules of expected value to show that Cov(aX + b, cY + d) 5 ac Cov(X, Y).
b. Use part (a) along with the rules of variance and standard deviation to show that Corr(aX + b, cY + d) 5 Corr(X, Y) when a and c have the same sign.
c. What happens if a and c have opposite signs?
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