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The absolute moment of M_n of a probability function P(x) taken about a point a is defined by M_n=int|x-a|^nP(x)dx.

A sequence of random variates X_0, X_1, ... is called absolutely fair if for n=1, 2, ..., <X_1>=0 and <X_(n+1)|X_1,...,X_n>=0 (Feller 1971, p. 210).

In probability, an event with Lebesgue measure 1.

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

A distribution with probability function P(x)=(x^(alpha-1)(1+x)^(-alpha-beta))/(B(alpha,beta)), where B is a beta function. The mode of a variate distributed as ...

An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

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 ...

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

Two events A and B are called independent if their probabilities satisfy P(AB)=P(A)P(B) (Papoulis 1984, p. 40).

A joint distribution function is a distribution function D(x,y) in two variables defined by D(x,y) = P(X<=x,Y<=y) (1) D_x(x) = lim_(y->infty)D(x,y) (2) D_y(y) = ...