An approximate variance for line intersection counts
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Let λ denote a rectifiable line in a plane for which the length per unit area is to be estimated by counting the intersections with random test lines dropped on the plane. The asymptotic distribution and variance of the number of intersections with a single test line is derived for a model which assumes λ to be the boundary of particles or random area. Numerical examples illustrate the applicability of the derived variance expression.
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