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# Let X and Y be 2 random normal variables N(0;1) and independant. Let R = sqrt(X 2 +Y 2 ) and = arctan(Y/X).

Let X and Y be 2 random normal variables N(0;1) and independant. Let R = sqrt(X 2 +Y 2 ) and θ = arctan(Y/X). Note that (R,θ) are polar coordinates of (X,Y)

Determine the marginal density function of R and of θ