All Questions
Tagged with geometric-probability uniform-distribution
18
questions
9
votes
2
answers
338
views
Probability that Mercury is the nearest planet to Earth.
Motivation: We tend to think of Venus as the nearest planet to Earth because at its nearest approach to Earth, Venus is the closest at 39 million Km away. This is followed by Mars at 56 million Km and ...
- 20.8k
1
vote
0
answers
53
views
Distances of points in unit square to N random anchor points
Assume that N points are distributed uniformly randomly within the unit square, and call these points anchor points.
What is the mean, mean minimum, and mean maximum distance of a point randomly ...
- 45
-1
votes
2
answers
188
views
Probability function for distance to the nearest neighbour given $n$ points distributed randomly on a line? [closed]
Note: I'm not familiar with a lot of mathematical terminology, so please excuse any misuses. I'd also make a request to use simpler language (if possible) in an answer
What I'm seeking is similar to ...
- 101
3
votes
1
answer
809
views
If $U$ is uniformly distributed on $S^{d-1} \subset \mathbb{R}^d$, what's the distribution of its orthogonal projection onto any vector?
Let $U \in S^{d-1} \subset \mathbb{R}^d$ follow a uniform distribution on a sphere. Let $v \in \mathbb{R}^d.$ Then is the orthogonal projection $U^{T}v=\langle U,v \rangle$ uniformly distributed, and ...
- 2,364
0
votes
1
answer
485
views
For $ x,y,z \in (0,1) $ chosen randomly with uniform distribution, what's the probability that $x+y+z<1$? [duplicate]
I tried the $2D$ case with $x,y \in (0,1)$ and $P(x+y < 1) = \frac{1}{2}$
I got this by sketching the inequalities in the question, namely $ 0\leq x,y\leq 1, $ and $y < 1-x$ and seeing that ...
3
votes
1
answer
173
views
Density of the first $k$ coordinates of a uniform random variable
Suppose that $X$ is distributed uniformly in the $n$-sphere $\sqrt{n}\mathbf{S}^{n-1} \subset \mathbf{R}^n$. Then apparently the distribution of $(X_1, \dots, X_k)$, the first $k < n$ coordinates ...
- 3,774
0
votes
1
answer
96
views
Probability two splits make triangle
This is a slight variation on the usual broken stick problem.
A stick is broken randomly into two pieces. The larger piece is then broken in two. What is the probability the pieces can form a ...
- 31
5
votes
1
answer
354
views
What is the probability that the larger of two independent uniform variables on $[0,1]$ is greater than $3/4$ if the smaller one is less than $1/4$?
Two independent random variables are uniformly distributed on $[0, 1]$.
The question asks if the smaller of the two numbers is strictly less than
$\frac{1}{4}$, then what is the probability that ...
- 130
1
vote
2
answers
77
views
What is the expected perimeter of the quadrilateral implied by choosing points uniformly on each side of a unit square?
On each side of a square with unit length sides choose a point uniformly. Connect these points to form a quadrilateral. What is the expected perimeter of this quadrilateral?
I am able to simulate ...
- 1,024
2
votes
1
answer
95
views
What is the expected length of the implied side and area formed by bending a unit length at a random point and angle?
What is the length of the length of the implied side and area of a triangle created by bending a unit length at a uniformly distributed point and angle? By simulation it seems that the expected length ...
- 1,024
6
votes
3
answers
244
views
What is the expected length of the hypotenuse formed by bending a unit length randomly at a right angle?
This is easy enough to simulate and find the answer is somewhere around .812. However I am not finding it so easy to solve the integral involved which I believe is...
$$\int_0^1 \sqrt{x^2+(1-x)^2} dx$...
- 1,024
5
votes
2
answers
2k
views
Average shortest distance between some random points in a box
Suppose there is a square box with side length $m$ (measured in pixels). Let there be $n$ points in this box, distributed uniformly within the box (with integer coordinates, aligned to a pixel grid). ...
- 51
3
votes
1
answer
626
views
Estimating number of points on convex hull constrained in a triangle
I am distributing points uniformly within an equilateral triangle:
I would like to make a guess, for any given number of distributed points, how many of those points on average will be on the convex ...
- 135
1
vote
0
answers
291
views
Uniform Coin Drop Probability
Suppose that we drop a round coin with a diameter of 1 cm onto a gigantic sheet of paper with red lines drawn vertically every 10 cm and blue lines drawn horizontally every 5 cm.
(i) What is the ...
- 167
2
votes
1
answer
464
views
Probability that n points on a circle are in one quadrant
Question
Points $A$,$B$ and $C$ are randomly chosen from a circle, What is
the probability that all the points are in one quadrant ($\frac{1}{4}$
circle)?
My try
Using this answer about ...
- 3,130