Linked Questions

1
vote
1answer
531 views

Compute average distance between numbers $0$ to $10$ [duplicate]

I'd like to calculate the average difference between two numbers, each between $0$ and $10$. I calculated this for integers and came up with an average distance of $4$. My method: there are $10$ ...
0
votes
3answers
87 views

Probability distribution difficult exercise [duplicate]

I have to solve this exercise and I have no idea how to do it... Help is highly appreciated. We make the following experiment: we ask 2 persons to write one real number from [0, 5] each on a ...
20
votes
4answers
4k views

Average distance from center of circle

Using calculus, we can show that the average distance of a point in a circle to the center is $2R/3$, where $R$ is the radius. However, I have a separate way of approaching this question through ...
14
votes
1answer
9k views

Average distance between two random points in a square

A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square? For more general "rectangle" case, see here. The proof found there is ...
9
votes
1answer
9k 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 ...
16
votes
1answer
3k views

How is the distance of two random points in a unit hypercube distributed?

Let $p_1, p_2 \sim U([0, 1]^n)$ with $n \in \mathbb{N}$ be two points in the $n$-dimensional unit hypercube which are uniform randomly independently sampled. How is the distance $d(p_1, p_2) = \sqrt{\...
2
votes
3answers
1k views

What is the expected distance between these two points?

Suppose you have a straight line of length L, and a point is chosen at random along the line. Now suppose a second point is chosen at random to the left of the first point. What is the expected ...
6
votes
2answers
305 views

Random points on interval, expected lengths of pieces

Many years ago I came across the following task. If we have the interval $[0; 1]$ and we throw $N$ uniformly distributed and mutually independent points on it, then we'll get $N+1$ segments. What is ...
0
votes
2answers
431 views

The expected distance to the nearest neighbor when N points are placed randomly on a line

In a prior post about the expected distance between two randomly selected points on a line of length L, this answer was given link. The visual representation for the answer $\frac{L}{3}$ was useful, ...
3
votes
1answer
353 views

Average distance detween two random points on two line segments

Suppose you have two straight line of length $L_1$ and $L_2$, and a point is chosen at random along each line. What is the expected distance between these points? This question is a complement of ...
0
votes
1answer
401 views

Expected distance between two points on randomly selected line segment

My question is similar to a question answered before many times, namely the expected distance of L/3 between two random points on a line segment (Average Distance Between Random Points on a Line ...
0
votes
1answer
81 views

What is the expected distance between two points? 1/3 or 1/4

I have come across two forum about expected distance between two points and found seemingly conflicting results. Which one is correct? If they are two different ways of saying the same thing, can ...
0
votes
1answer
93 views

Average distance between consecutive points in a one-dimensional auto-correlated sequence

Case A. Simplest problem: Choose two points from the unit interval according to a uniform random distribution. The average distance between them is one-third, as shown in a related question. Case B. ...
1
vote
1answer
45 views

Distribution of average distances to a point on a line segment

my question is somewhat related to this one here, where the expected value of the distance $d$ of two uniformly drawn points from an interval $[0;L]$ is sought. It's $\frac{L}{3}$ and the pdf should ...
3
votes
1answer
49 views

Expected least distance between closest two points out of $n$ drawn from a distribution

Suppose I draw $n$ points in $\mathbb{R}$ from a distribution $p$. What is the expected least distance between two of the points drawn? I am particularly interested in the uniform distribution $\...

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