“Point-Point Distance--1-D”的概念、定义、习题解题方法及翻译-数学辞典

单词

Point-Point Distance--1-D

释义

Point-Point Distance--1-D

Given a unit Line Segment , pick two points at random on it. Call the first point and the secondpoint . Find the distribution of distances between points. The probability of the points being a(Positive) distance apart (i.e., without regard to ordering) is given by



			(1)

where

is the Dirac Delta Function and

is the Heaviside Step Function. The Momentsare then





			(2)

giving Moments about 0

			(3)
			(4)
			(5)
			(6)

The Moments can also be computed directly without explicit knowledge of the distribution








			(7)





			(8)

The Moments about the Mean are therefore

			(9)
			(10)
			(11)

so the Mean, Variance, Skewness, and Kurtosis are

			(12)
			(13)
			(14)
			(15)

The probability distribution of the distance between two points randomly picked on a Line Segment is germane to theproblem of determining the access time of computer hard drives. In fact, the average access time for a hard drive is preciselythe time required to seek across 1/3 of the tracks (Benedict 1995).

See also Point-Point Distance--2-D, Point-Point Distance--3-D, Point-Quadratic Distance, Tetrahedron Inscribing, Triangle Inscribing in a Circle

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 930-931, 1985.

Benedict, B. Using Norton Utilities for the Macintosh. Indianapolis, IN: Que, pp. B-8-B-9, 1995.

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