Bivariate standard normal distribution with correlation

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Let X and Y have a bivariate standard normal distribution with correlation ρ = 0. That is, X and Y are independent. Let (x, y) be a point in the plane. The rotation of (x, y) about the origin by angle θ gives the point

Show that the joint density of X and Y has rotational symmetry about the origin. That is, show that f(x, y) = f(u, v).

Reference no: EM131107018

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