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Let X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its...

Let X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its polar coordinates, i.e. X1 = R cos(Θ) and X2 = R sin(Θ). Show that X is spherically symmetric if and only if R and Θ are independent, and Θ ∼Uniform(0, 2π).

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