Search Results for ""

The mean triangle area of a triangle picked at random inside a unit cube is A^_=0.15107+/-0.00003, with variance var(A)=0.008426+/-0.000004. The distribution of areas, ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

Let X_1, ..., X_N be a sequence of independent observations of a random variable X, and let the number of observations N itself be chosen at random. Then Wald's equation ...

A continuous-time stochastic process W(t) for t>=0 with W(0)=0 and such that the increment W(t)-W(s) is Gaussian with mean 0 and variance t-s for any 0<=s<t, and increments ...

A sequence of random variates X_0, X_1, ... is called absolutely fair if for n=1, 2, ..., <X_1>=0 and <X_(n+1)|X_1,...,X_n>=0 (Feller 1971, p. 210).

A limiting value of a holonomic function near a singular point. Holonomic constants include Apéry's constant, Catalan's constant, Pólya's random walk constants for d>2, and ...

A "law of large numbers" is one of several theorems expressing the idea that as the number of trials of a random process increases, the percentage difference between the ...