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The binomial distribution gives the discrete probability distribution P_p(n|N) of obtaining exactly n successes out of N Bernoulli trials (where the result of each Bernoulli ...

Champernowne's constant C=0.12345678910111213... (1) (OEIS A033307) is the number obtained by concatenating the positive integers and interpreting them as decimal digits to ...

An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...