Questions tagged [geometric-probability]
Probabilities of random geometric objects having certain properties (enclosing the origin, having an acute angle,...); expected counts, areas, ... of random geometric objects. For questions about the geometric distribution, use (probability-distributions) instead.
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probablity of random pick up three points inside a regular triangle which form a triangle and contain the center
what is the probablity of random pick up three points inside a regular triangle
which form a triangle and contain the center of the regualr triangle
the three points are randomly picked within the ...
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Average area of choosing three points on a surface?
Assume I choose three random points on the surface of a sphere. What is the average area? (Each point is independently chosen relative to a uniform distribution on the sphere) Also, what would be the ...
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Probability on an infinite plane
(I thought this is a popular problem, but sadly Google yields nothing.)
Three points are chosen at random on an infinite plane. What is the probability that they are on a line?
And a variant: the ...
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What is the probability that a quadrilateral is convex?
Given $4$ distinct randomly chosen points $x_1$, $x_2$, $x_3$, and $x_4$ in the plane such that the polygonal path from $x_1$ to $x_2$ to $x_3$ to $x_4$ to $x_1$ describes a non-self-intersecting ...
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Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$
A scheme to generate random variates distributed uniformly in $S^2=\{x\in \mathbb{R}^n \mid \|x\|_2=1\}$ is well known: generate a standard normal variate in $\mathbb{R}^n$ and normalize it to unit ...
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Expectancy value for the percentage of points lying in the Convex Hull (3D)
Suppose I chose n uniformly distributed random points in a 3D cube. What is the expected value for the percentage of points lying on the convex hull as a function of n?
Just as a reference, I made ...
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What is average distance from center of square to some point?
How can I calculate average distance from center of a square to points inside the square?
Newcommer
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Probability that the convex hull of random points contains sphere's center
What is the probability that the convex hull of $n+2$ random points on $n$-dimensional sphere contains sphere's center?
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