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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 ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

In probability, an event with Lebesgue measure 1.

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

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 ...

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

A generalized mobile automaton is a generalization of the mobile automaton in which the automaton may have more than one active cell. Generalized mobile automata allow for ...

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

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