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(12 points) X and Y are identically distributed random variables with.pdf

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X and Y are random variables with expected values of 0, covariance of 3, and correlation of 1/2. U and V are defined as linear transformations of X and Y with constants a and b. The covariance of U and V is a*b*3. The correlation of U and V is 1/2. U and W will be uncorrelated if a=-b.

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(12 points) X and Y are identically distributed random variables with E[X]=E[Y]=0 and covariance COV(X,Y)=3 and correlation coefficient X,Y=1/2. For nonzero constants a and b,U=aX,V=bY. (a) (4 pts) Find COV(U,V). (b) (4 pts) Find the correlation coefficient U,V. (c) (4 pts) Let W=U+V. For what values of a and b can make X and W uncorrelated?

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