51. Let X and Y denote the coordinates of a point uniformly chosen in the disk of...

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

$$

f(x,y) = \frac{1}{\pi}

$$

x² + y² ≤ 1 Find the joint density function of the polar coordinates R = (X² + Y²)¹/² and Θ = tan⁻¹Y/X.

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A First Course In Probability

ISBN: 9780137463145

5th Edition

Authors: Sheldon M. Ross

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