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For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

A well-formed formula B is said to be true for the interpretation M (written |=_MB) iff every sequence in Sigma (the set of all denumerable sequences of elements of the ...

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

The number of nondecreasing lists {a_1,a_2,...,a_n} consisting of n elements 1<=a_i<=k is given by the binomial coefficient N(n,k)=(n+k-1; n-1). For example, there are six ...

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.