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The metric properties discovered for a primitive figure remain applicable, without modifications other than changes of signs, to all correlative figures which can be ...

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

A Markov chain is collection of random variables {X_t} (where the index t runs through 0, 1, ...) having the property that, given the present, the future is conditionally ...

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

(d^2V)/(dv^2)+[a-2qcos(2v)]V=0 (1) (Abramowitz and Stegun 1972; Zwillinger 1997, p. 125), having solution y=C_1C(a,q,v)+C_2S(a,q,v), (2) where C(a,q,v) and S(a,q,v) are ...

A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, e.g., x, 3xy^2, or -2x^2y^3z. A monomial can also be ...