Search Results for ""

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

A set of positive integers S is called sum-free if the equation x+y=z has no solutions x, y, z in S. The probability that a random sum-free set S consists entirely of odd ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...