Geometric ProbabilitySIAM, 1978年6月1日 - 180 頁 Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; and much more. |
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Alikoski asymptotic axis boundary Buffon C₁ cell nucleus chords intersect chromosomes circumference consider convex curve convex hull convex region coordinates cos² coverage covered Crofton's Crofton's formula derive distance dP₁ E(Area OXY equation expected number four random points fragments function geometrical probability given half angle half sphere Hence hits independent integral intercepts an arc invariant isotropic K₁ length line segment mean area measure needle number of intersections number of sides observer car obtain P(AB P[same side P₁ pair perimeter perpendicular plane point falls Poisson distribution Poisson field Poisson process polygon positions Pr RQ problem r₁ random arcs random cap random chord random lines intersecting random variable randomization model randomly re-entrant quadrilateral rectifiable curves result rigid motions S₁ sin² spherical cap sufficient statistic surface tetrahedron theorem total number uniformly distributed V₁ V₂ volume x-axis Σ Σ