Let X and Y be random variables, and a and b be constants a Prove that Cov(aX, bY ) ab Cov(X,Y ) b Prove that if a 0 and b 0, then aX,bY X,Y Conclude that the correlation coefficient is unaffected by changes in units

Question: Let X and Y be random variables, and a and b be constants. a. Prove that Cov(aX, bY ) = ab Cov(X,Y ). b. Prove

Let X and Y be random variables, and a and b be constants.
a. Prove that Cov(aX, bY ) = ab Cov(X,Y ).
b. Prove that if a > 0 and b > 0, then ρaX,bY = ρX,Y. Conclude that the correlation coefficient is unaffected by changes in units.

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