# Question

Let X and Y denote the coordinates of a point uniformly chosen in the circle of radius 1 centered at the origin. That is, their joint density is

f(x, y) = 1/π x2 + y2 ≤ 1

Find the joint density function of the polar coordinates

R = (X2 + Y2)1/2 and Θ = tan−1 Y/X.

f(x, y) = 1/π x2 + y2 ≤ 1

Find the joint density function of the polar coordinates

R = (X2 + Y2)1/2 and Θ = tan−1 Y/X.

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