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Informally, the sample space for a given set of events is the set of all possible values the events may assume. Formally, the set of possible events for a given random ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function R_2(r) for the zeros of the Riemann zeta function zeta(z) on the ...

For two random variates X and Y, the correlation is defined bY cor(X,Y)=(cov(X,Y))/(sigma_Xsigma_Y), (1) where sigma_X denotes standard deviation and cov(X,Y) is the ...

If a sequence takes only a small number of different values, then by regarding the values as the elements of a finite field, the Berlekamp-Massey algorithm is an efficient ...

The weak law of large numbers (cf. the strong law of large numbers) is a result in probability theory also known as Bernoulli's theorem. Let X_1, ..., X_n be a sequence of ...

A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information ...