25. Let (X,Y) be uniformly distributed in a circle of radius r about the origin. That is,...
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25. Let (X,Y) be uniformly distributed in a circle of radius r about the origin. That is, their joint density is given by
Let R = 0 X2 + Y2 and θ = arc tan Y/X denote their polar coordinates. Show that R and θ are independent with θ being uniform on (0, 2π) and P{R
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