average seek time | distance between points | distance between two points | point-point distance--1-dimensional | seek time | two-point distance

Given a unit line segment [0, 1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The probability density function for the points being a (positive) distance d apart (i.e., without regard to ordering) is given by P(d) | = | ( integral_0^1 integral_0^1 δ(d - left bracketing bar x_2 - x_1 right bracketing bar ) d x_1 d x_2)/( integral_0^1 integral_0^1 d x_1 d x_2) | = | 2(1 - d), where δ(x) is the delta function. The distribution function is then given by D(d) = d(2 - d). Both are plotted above.

geometric probability | point-point distance--2-dimensional | point-point distance--3-dimensional | point-quadratic distance | sphere point picking | triangle line picking