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This was a question I created (I don't even know if this has an answer), but I don't know how to proceed (I considered an argument where a point might be more likely to be chosen inside than outside, but this didn't work).

Any thoughts on how to proceed?

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    $\begingroup$ First you need to define how you select points at random since there is no uniform distribution on the whole plane. The question has been asked when you pick uniformly in a square and even for smallish values of $n$ ($5$ or $6$ ?) we don't know the numbers. They're hidden between giant nested integrals. $\endgroup$ – mercio Nov 13 '17 at 8:37
  • $\begingroup$ @mercio I added the condition that the points are inside a Jordan Curve. $\endgroup$ – Sharky Kesa Nov 13 '17 at 9:11

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