Question: Consider the following attempt at generating a point uniformly distributed in the circle of radius 1 centered at the origin. In polar coordinates, pick R

Consider the following attempt at generating a point uniformly distributed in the circle of radius 1 centered at the origin. In polar coordinates, pick R uniformly at random on (0,1). Pick Θ uniformly at random on (0, 2π), independently of R. Show that this method does not work. That is show (R, Θ) is not uniformly distributed on the circle.

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