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Notes on random chords in convex bodies
- Part of
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- Journal:
- Journal of Applied Probability / Volume 30 / Issue 4 / December 1993
- Published online by Cambridge University Press:
- 14 July 2016, pp. 889-897
- Print publication:
- December 1993
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- Article
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Consider a compact body E embedded in a convex compact body G. A point P is randomly chosen in E and three different rays to the boundary ∂G of G are generated by P. Ray
is in a uniformly random direction and has length R, ray 
is through a second random point chosen from within G and has length W, and ray 
is to a random point in ∂G and has length Y. The distribution of Y is obtained and is related to previous work. When E is specialized to G or to ∂G, other known results are retrieved. The paper ends with a discussion of a conjecture relating the means of R, W and Y.
is in a uniformly random direction and has length 
is through a second random point chosen from within 
is to a random point in 