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A Problem on Random Paths

Published online by Cambridge University Press:  03 November 2016

W H. McCrea
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Extract

The general problem. This paper deals with particular cases of the following problem: A rectangular array of square cells is given; a particle P moves from one cell to another in such a way that, when it is in any cell, it is equally likely to pass across any of its edges. P is liberated in any given cell, and it is required to find the probability that it will ultimately emerge across any stated edge in the boundary of the array.

Type
Research Article
Information
The Mathematical Gazette , Volume 20 , Issue 241 , December 1936 , pp. 311 - 317
Copyright
Copyright © Mathematical Association 1936

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References

page no 311 note * Ball, W. W Rouse, Mathematical Recreations and Essays (9th ed., 1920), 135 Google Scholar; Borel, E., Calcul des Probabilités, Tome 1, Fasc. 1 (1925), Ch. VGoogle Scholar

page no 311 note † Rayleigh, , Scientific Papers, V, 256 Google Scholar.