6
votes
0answers
185 views

What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
0
votes
2answers
308 views

How to recognize ellipse/ellipsoid from random points? UN-weighted average?

Suppose we are getting random points in 2D (or 3D) which tend to be on ellipse (or ellipsoid). We can't guarantee points are uniformly distributed over ellipse (ellipsoid surface). The task is to ...
3
votes
2answers
1k views

Average Distance Between Random Points in a Rectangle

My question is similar to this one but for rectangles instead of lines. Suppose I have a rectangle with sides of length $L_w$ and $L_h$. What is the average distance between two uniformly-distributed ...
3
votes
1answer
259 views

Average sine of an angle between two rays in a cone

I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle. Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
3
votes
2answers
1k views

Average distance between two points in a circular disk

How can I find an average distance between two points lying inside a circular disk of a certain radius? I wonder if there is any other way except of using a Monte Carlo method?
1
vote
1answer
48 views

Variant of the modal average

I know that there are variants of the arithmetic mean and the median that are applicable to three dimensional data (centroid and medoid), but have not been able to find such a thing for the modal ...
4
votes
1answer
315 views

Average over angles

I feel quite dumb for asking this, but it's getting a bit frustrating. I have a function which depends on $\theta$ and $\phi$ in spherical coordinates: $$ f(\theta, \phi) = \sin^2 \theta ...
4
votes
2answers
1k views

Find the average of a collection of points (in 2D space)

I'm a bit rusty on my math, so please forgive me if my terminology is wrong or I'm overlooking extending a simple formula to solve the problem. I have a collection of points in 2D space (x, y ...