Search Results for ""

An experiment in which s trials are made of an event, with probability p of success in any given trial.

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

The two-dimensional Hammersley point set of order m is defined by taking all numbers in the range from 0 to 2^m-1 and interpreting them as binary fractions. Calling these ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...