Given two original random variables x and y suppose that we, Ask an Expert

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Given two original random variables X and Y, suppose that we modify one of them by adding a constant: W = a + X. How does cov(W,Y) compare to cov(X,Y)?

a. Use algebra and linearity of the expectation operator to find the answer.

b. Explain how the transformation affects the drawing of the scatterplot we used to develop our understanding of covariance, and therefore why the answer to part a. should be expected.

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