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The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

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.

The nonconservation of adiabatic invariants which arises in systems with three or more degrees of freedom.

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

If a field has the property that, if the sets A_1, ..., A_n, ... belong to it, then so do the sets A_1+...+A_n+... and A_1...A_n..., then the field is called a Borel field ...

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, ...

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

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 ...

An experiment E(S,F,P) is defined (Papoulis 1984, p. 30) as a mathematical object consisting of the following elements. 1. A set S (the probability space) of elements. 2. A ...