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Let X and Y be independent N(0,1) RVs. Suppose U = (X+Y)/squareroot(2) and V = (X-Y)/squareroot(2)....

Let X and Y be independent N(0,1) RVs. Suppose U = (X+Y)/squareroot(2) and V = (X-Y)/squareroot(2).

Please derive the joint distribution of (U, V ) by using the Jacobian matrix method.

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