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Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

The distribution of a product of two normally distributed variates X and Y with zero means and variances sigma_x^2 and sigma_y^2 is given by P_(XY)(u) = ...

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.

The bias of a series is defined as Q[a_i,a_(i+1),a_(i+2)]=(a_ia_(i+2)-a_(i+1)^2)/(a_ia_(i+1)a_(i+2)). A series is geometric iff Q=0. A series is artistic iff the bias is ...

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2) where delta(x) ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

"Jabulani polyhedron" is a term introduced here to refer to the polyhedron illustrated above which underlies the shape of the soccer ball used in the 2010 World Cup in South ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...