Exercise: Correlation properties

As in the preceding example, let Z, V, and W be independent random variables with mean 0 and variance 1, and let X = Z + V and Y = Z + W. We have found that p (X, Y) = 1/2. a) It follows that: P ( X, - Y) = P ( - X, - Y ) = b) Suppose that X and Y are measured in dollars. Let X' and Y"' be the same random variables, but measured in cents, 50 that X"' = 100X and Y' = 100Y. Then, P ( X' , Y') = () Suppose now that X" = 3Z + 3V + 3 and Y = -2Z -2W. Then P ( X , Y ) = d) Suppose now that the variance of Z is replaced by a very large number. Then p (X, Y) is close to e) Alternatively, suppose that the variance of Z is close to zero. Then p (X, Y) is close to