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On the length distribution of stochastic subarcs of a rectifiable arc
J. E. Mann
Journal:

Journal of Applied Probability / Volume 14 / Issue 3 / September 1977

Published online by Cambridge University Press:

14 July 2016, pp. 654-660

Print publication:

September 1977
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Suppose that A1, A2, · ··, An are disjoint subarcs of a rectifiable arc A ⊆ Rk. The location and length of each subarc are assumed to be continuous random variables. An expression for the expected fraction of A covered by subarcs each of length greater than τ ≧ 0 is obtained and applied to two conceptually distinct problems associated with light penetration of an absorbing medium.

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On the length distribution of stochastic subarcs of a rectifiable arc