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Q6Section A (Section A)6 of 60

Uncorrelated linear combinations

Let (X,Y)(X,Y) be a random vector with Var⁡(X)=Var⁡(Y)=1\operatorname{Var}(X)=\operatorname{Var}(Y)=1 and Cov⁡(X,Y)=−0.5\operatorname{Cov}(X,Y)=-0.5. For which one of the following values of bb, the random variables U=bX+YU=bX+Y and V=X+bYV=X+bY are uncorrelated?

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