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Jan 25, 2016 at 21:40 comment added BruceET Notice that the arcsine distribution in @Did's Comment (for the circumference) has modes at each end--sometimes said to be 'bathtub shaped'. Anyhow, very much different from the distribution of my Answer (for the disk). The interpretation really does matter.
Jan 25, 2016 at 20:30 comment added Did "I believe that the problem is a little more difficult if the points are distributed at random on the circumferencecircumference of the unit circle" Not much, the result is the well known arcsine distribution.
Jan 25, 2016 at 20:27 history edited BruceET CC BY-SA 3.0
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Jan 25, 2016 at 20:22 history answered BruceET CC BY-SA 3.0