MHB Compute probability closeness between points in a 2D surface

[LucaDanieli]

Hi all,

Sorry, in my first message, I posted this question in the Basic Probability section, and so I moved it to this section.

I have a surface (for example, a blank paper).
In this surface, I have some elements of the set "A" randomly distributed.
In this surface, I also have some elements of the set "B" randomly distributed.
I would like to understand how may elements of "B" are present within a ray X from any element of "A".

I mean something like: "for each element An, there are N% (probability_result) elements of "B". "

Is it possible?

 

[Joppy]

I would like to understand how may elements of "B" are present within a ray X from any element of "A".

Possibly need more information. Without more information about the ray, it seems you want to find the diameter of B and relate it to A in some way. What are you trying to do exactly?

 

[LucaDanieli]

Hi Joppy,

thank you for your reply. Indeed I am not a mathematician so I was not able to understand how much information you need. I have improved the explanation in this Stackoverflow thread: https://math.stackexchange.com/questions/3403515/compute-probability-closeness-points-within-2d-surface?noredirect=1#comment7002121_3403515

Does it help understanding my question?

 

[Joppy]

I think by "ray" you mean "radius"? So perhaps the question is: given a sequence of points representing circle centers ($A_n$) with radii $r$ and a collection of points $B_m$, what proportion of points $B_n$ are contained within each circle centered at $A_n$?

 

[LucaDanieli]

Hi Joppy,

thanks for clarifying. Indeed it's radius and not ray. (I guess "ray" indicates the sunlight... in Italian they have the same term).
So the final question is exactly as you summarized.

So: given a sequence of points representing circle centers (A_n) with radii r and a collection of points B_m, what proportion of points B_n are contained within each circle centered at A_n ?

Thanks also for making terminology more correct.