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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 plot of y_i versus the estimator e_i=y^^_i-y_i. Random scatter indicates the model is probably good. A pattern indicates a problem with the model. If the spread in e_i ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

A sequence of random variates X_0, X_1, ... with finite means such that the conditional expectation of X_(n+1) given X_0, X_1, X_2, ..., X_n is equal to X_n, i.e., ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

A random process whose future probabilities are determined by its most recent values. A stochastic process x(t) is called Markov if for every n and t_1<t_2...<t_n, we have ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...