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Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...

The nth raw moment mu_n^' (i.e., moment about zero) of a distribution P(x) is defined by mu_n^'=<x^n>, (1) where <f(x)>={sumf(x)P(x) discrete distribution; intf(x)P(x)dx ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

A series is called artistic if every three consecutive terms have a common three-way ratio P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)). A series is ...

A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.