|
A conditional event algebra (CEA) is an algebraic structure whose domain consists of logical objects described by statements of forms such as "If ''A'', then ''B''," "''B'', given ''A''," and "''B'', in case ''A''." Unlike the standard Boolean algebra of events, a CEA allows the defining of a probability function, ''P'', which satisfies the equation ''P''(If ''A'' then ''B'') = ''P''(''A'' and ''B'') / ''P''(''A'') over a usefully broad range of conditions. ==Standard probability theory== In standard probability theory, one begins with a set, Ω, of outcomes (or, in alternate terminology, a set of possible worlds) and a set, ''F'', of some (not necessarily all) subsets of Ω, such that ''F'' is closed under the countably infinite versions of the operations of basic set theory: union (∪), intersection (∩), and complementation ( ′). A member of ''F'' is called an event (or, alternatively, a proposition), and ''F'', the set of events, is the domain of the algebra. Ω is, necessarily, a member of ''F'', namely the trivial event "Some outcome occurs." A probability function ''P'' assigns to each member of ''F'' a real number, in such a way as to satisfy the following axioms: : For any event ''E'', ''P''(''E'') ≥ 0. : ''P''(Ω) = 1 : For any countable sequence ''E''1, ''E''2, ... of pairwise disjoint events, ''P''(''E''1 ∪ ''E''2 ∪ ...) = ''P''(''E''1) + ''P''(''E''2) + .... It follows that ''P''(''E'') is always less than or equal to 1. The probability function is the basis for statements like ''P''(''A'' ∩ ''B''′) = 0.73, which means, "The probability that ''A'' but not ''B'' is 73%." 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「conditional event algebra」の詳細全文を読む スポンサード リンク
|