Let X And Y Be Independent N 0 1 Rvs Suppose U X Y Root 2 And U X Y Root2 A Comp

Let X and Y be independent N(0; 1) RVs. Suppose U =X+Y/root 2and U =X-Y/root2a. Compute E[U], V ar(U), E[V ], V ar(V ), E[UV ].b. Derive the joint distribution of (U; V ) by using the Jacobian matrix method.

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