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If there were a square field that is $x$ km wide and long, and there are $y$ objects in the field, is there a way to calculate the average distance between each object?

I tried $\frac{x}{\sqrt{y}}$, but it didn't seem right. If it is, please correct me.

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someguy
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  • How are your objects supposed to be distributed in the field? – mathcounterexamples.net Feb 10 '21 at 14:00
  • Are you saying that the $y$ objects are placed randomly in the field? – Rushabh Mehta Feb 10 '21 at 14:01
  • I don't quite understand what you are referencing to as "average distance". Let's say each object is represented by a $2$-dimensional random vector $V_i$, so that we have $V_1,\cdots, V_y$, and let's say we know everything about the $2y$-dimensional random vector $(V_1,\cdots, V_y)$. Do you want to know $E(\lvert V_i-V_j\rvert)$ for all $i<j$? Do you want to know $\frac{2}{y(y-1)}E\left(\sum_{1\le i<j\le y}\lvert V_i-V_j\rvert\right)$? Or do you want to know the law of the random variable $\frac{2}{y(y-1)}\sum_{1\le i<j\le y}\lvert V_i-V_j\rvert$? –  Feb 10 '21 at 14:11
  • the y objects are placed randomly on the field. – someguy Feb 10 '21 at 14:12
  • @Gae.S. Sorry i dont really know im 10 years old ;-; – someguy Feb 10 '21 at 14:13
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    @someguy Then you shouldn't be here because stackexchange forums are for thirteen-year-old people or older. –  Feb 10 '21 at 14:14
  • I would like to redirect you to this thread: https://math.stackexchange.com/questions/1254129/average-distance-between-two-random-points-in-a-square?rq=1 It asks pretty much the same question but there are only two points. Though if your question means the average distance between two random points on the field it would give the same answer as to the aforementioned question, which already was answered. – Saha Feb 10 '21 at 14:18
  • possible duplicate: https://math.stackexchange.com/q/3974671/617446 – user619894 Feb 10 '21 at 15:36

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