A point is generated on a unit disk in the following way:
Chapter , Problem 55(choose chapter or problem)
A point is generated on a unit disk in the following way: The radius, R, is uniform on [0, 1], and the angle \(\Theta\) is uniform on \([0, 2 \pi]\) and is independent of R.
a. Find the joint density of \(X = R \cos \Theta\) and \(Y = R \sin \Theta\).
b. Find the marginal densities of X and Y.
c. Is the density uniform over the disk? If not, modify the method to produce a uniform density.
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