Question: Give conditions on a > 0, b > 0, and u so that fX,Y(x, y) = ke(ax22uxy+by2) is the bivariate normal density of random variables

Give conditions on a > 0, b > 0, and u so that
fX,Y(x, y) = ke−(ax2−2uxy+by2)
is the bivariate normal density of random variables X and Y each having expected value 0. Also, find Var(X), Var(Y), and ρ(X, Y).

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