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Size: 332 KB
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Title: Odds and Integrals
Book
Description: This
WorkBook explores the following question. Given n random numbers chosen
from the unit interval [0,1], what is the expected value of the kth shortest
segment so determined?
It translates this problem from probability to geometry and shows how
a certain extension of the notion of trapezoid may be used to calculate
certain integrals of functions defined on simplices and depending on the
barycentric coordinates of the points.
As always, the emphasis is on visualization through experimentation. The
reader may do the suggested experiment and see for herself the strange
distribution of expected lengths. Then the reader may construct triangles
in the plane, and examine the properties of the associated first barycentric
subdivision.
Author: James E. White
Suggested Use: The WorkBook is fully documented in the 19 page documentaion file that accompanies it. That printable file contains hardcopy of all text and lectures. Experiment with probability, topology, and graphics
Topics: probability, integration, approximation, geometry, Geometric Construction, vectors, permutations, barycentric, topology, simplex, simplicial complex, subdivision
Number of Pages: 8
Animation: Yes
Grade
Level: 