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The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

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

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true (usually that observations are the result of chance). ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The omega constant is defined as W(1)=0.5671432904... (1) (OEIS A030178), where W(x) is the Lambert W-function. It is available in the Wolfram Language using the function ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...