Covering a circle randomly with arcs has been well studied in the past (Geometric Probability - Solomon).

But the problem when the circle is changed to a line segment doesn't seem to have been studied before.

I'd like to know if there's any work out there who already obtained the probability distribution of the number and the length of the connected line segments that you get when randomly covering a line segment with another set of shorter segments, which may all be of equal length or have some kind of distribution.

Thanks!

PLEASEindicate this in your question. That way we avoid duplicated effort – Yemon Choi Feb 28 '12 at 6:22