Question: Let X = (X1, X2)^(transpose) be a two-dim random vector, and (R, ) be its polar coordinates, i.e. X1 = R cos() and X2 =

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

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