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A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let chi_m^2 and chi_n^2 be independent variates ...

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 ...

Consider the sample standard deviation s=sqrt(1/Nsum_(i=1)^N(x_i-x^_)^2) (1) for n samples taken from a population with a normal distribution. The distribution of s is then ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

A number of attractive tetrahedron 5-compounds can be constructed. The first (left figures) is one of the icosahedron stellations in which the 5×4 vertices of the tetrahedra ...

Probability and Statistics

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

alpha=1/Nsum_(i=1)^N|x_i-mu|=<|x_i-mu|>.