Geometrical Probability |
Contents
DISTRIBUTIONS OF POINTS IN EUCLIDEAN SPACE | 24 |
Random points in three dimensions | 47 |
Distribution of two points in a sphere | 53 |
Copyright | |
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Common terms and phrases
A₁ axis C₂ centre characteristic function chords of C₁ circle of radius consider convex figure convex region Crofton's defined diameters distance distributed at random dx dy E₁ element equal equation estimate Euclidean space expected number function geometrical probability given gonal Hence integral Jacobian joint distribution l₁ lattice points Lebesgue measure lines intersecting matrix mean free path mean value method needle non-overlapping number of intersections number of points obtained orthogonal orthogonal matrix P₁ P₂ particles perimeter perpendicular plane point inside Poisson distribution Poisson field polar coordinates prob probability density probability distribution probability measure problem R₁ random chord random lines random points random variable rotation solid angle sphere square Suppose T₁ theorem theory three dimensions three-dimensional space tion transformation triangle uniformly distributed variance vector Y₁ zero дх