Quote:
Originally Posted by Ether
The difference is in how you choose samples.
If you want the average distance between all unordered pairs of points, then you choose coordinates of pairs of points from a uniform random distribution, and compute the corresponding distance.
If you want the average length of all segments, you randomly choose a segment length, a segment orientation, and the coordinates of the center of the segment. Then you discard any chosen segments which are not inside the square. If you run a Monte Carlo sim of that, you'll get 0.3363
...and you'll get a pdf of L only, if you make a histogram of the data and adjust it to have an area of 1.
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How practical of you
I'd like to think it's possible to parametrize the choice of line segment by end points. Curious about the difference between that and the problem (simply choosing uniformly distributed end points) that we wrote 94 posts about. Obviously the end points of all line segments are not uniformly distributed in the square.
I've got an idea for finding just what their distribution is that I might get to if ever get unswamped this week.
The question is like asking "Is it better to drive by looking at a map the whole time or by remembering where you want to go and watching the road instead?" - lukevanoort [more] 
22-08-2016, 19:32
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