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A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

pi has decimal expansion given by pi=3.141592653589793238462643383279502884197... (1) (OEIS A000796). The following table summarizes some record computations of the digits of ...

The converse of Fisher's theorem.

Let S be partitioned into r×s disjoint sets E_i and F_j where the general subset is denoted E_i intersection F_j. Then the marginal probability of E_i is ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...