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Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

Correlation is the degree to which two or more quantities are linearly associated. In a two-dimensional plot, the degree of correlation between the values on the two axes is ...

The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

An unsolvable problem in logic dating back to the ancient Greeks and quoted, for example, by German philosopher Carl von Prantl (1855). The dilemma consists of a crocodile ...

Let M(h) be the moment-generating function, then the cumulant generating function is given by K(h) = lnM(h) (1) = kappa_1h+1/(2!)h^2kappa_2+1/(3!)h^3kappa_3+..., (2) where ...

Let phi(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a=b=1, phi(t) = ...