Jones (1999) looked at the distribution of functions of X and Y when X = R cos

Question:

Jones (1999) looked at the of functions of X and Y when X = R cos θ and Y = R sinθ, where θ ~ U{0, 2π) and R is a positive random variable. Here are two of the many situations that he considered.
(a) Show that X/Y has a Cauchy Show that the of (2XY)/√X2 + Y2 is the same as the of X. Specialize this result to one about n(0, σ2) random variables.
Distribution
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