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A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...

Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1=x_1,...,X_n=x_n)=(N!)/(product_(i=1)^(n)x_i!)product_(i=1)^ntheta_i^(x_i) (1) where x_i are ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

A variable with a beta binomial distribution is distributed as a binomial distribution with parameter p, where p is distribution with a beta distribution with parameters ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

The Zipf distribution, sometimes referred to as the zeta distribution, is a discrete distribution commonly used in linguistics, insurance, and the modelling of rare events. ...

The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...