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Results tagged with geometric-probability
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user 1131
2
votes
Minimum distance to a sampled point with given pdf
The heuristics behind that answer is the following. Consider the probability $P(r)$ that this distance is at least $r$. If equals $\int_Q (1-U(x,r))^N\,dx$ where $U(x,r)=\int_{B(x,r)}f(x)\,dx$. Now, $ …
- 61.9k
14
votes
Is there a set of point $S \subset \mathbb R^2$ such that $|\{C: C \text{ is unit circle bou...
An alternative solution is the following:
Take 10 unit vectors in the generic position. Consider all $1024$ possible sums from the empty one (the zero vector) to the full sum of all $10$ vectors. Colo …
- 61.9k
2
votes
Accepted
Expected triangle area of normal distributed vertices with colinear expectations
How was your formula derived?
You can do most of the work in your head without touching pen or paper. First, project to a random plane. Then the area will drop twice on average (Archimedes), so the an …
- 61.9k