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Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...

A distribution which arises in the study of integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)-1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)-1) = ...

The equation f(x_n|x_s)=int_(-infty)^inftyf(x_n|x_r)f(x_r|x_s)dx_r which gives the transitional densities of a Markov sequence. Here, n>r>s are any integers (Papoulis 1984, ...

A gambling game played at carnivals in which a player may bet on any one of the numbers 1 through 6. Three dice are then rolled and, if his number appears, he receives back a ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

A function that joins univariate distribution functions to form multivariate distribution functions. A two-dimensional copula is a function C:I^2->I such that C(0,t)=C(t,0)=0 ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...

If x_1/n_1 and x_2/n_2 are the observed proportions from standard normally distributed samples with proportion of success theta, then the probability that ...

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...