Téori probabilitas: Béda antarrépisi

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Ngarapihkeun éjahan, replaced: ngarupakeun → mangrupa, yen → yén using AWB
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m (Ngarapihkeun éjahan, replaced: ngarupakeun → mangrupa, yen → yén using AWB)
'''Téori probabilitas''' ngarupakeunmangrupa élmu [[matematik]] ngeunaan [[probabilitas]] atawa kamungkinan.
 
Matematikawan mikirkeun yenyén probabiliti salaku angka dina interval tina 0 ka 1 keur nangtukeun "kajadian" numana bener-bener kajadian atawa henteu kajadian dina bentuk acak. Probabilitas <math>P(E)</math> nangtukeun kajdian <math>E</math> dumasa kana [[aksioma probabilitas]].
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The probability that an event <math>E</math> occurs ''given'' the known occurrence of an event <math>F</math> is the '''[[conditional probability]]''' of <math>E</math> '''given''' <math>F</math>; its numerical value is <math>P(E \cap F)/P(F)</math> (as long as <math>P(F)</math> is nonzero). If the conditional probability of <math>E</math> given <math>F</math> is the same as the ("unconditional") probability of <math>E</math>, then <math>E</math> and <math>F</math> are said to be [[statistical independence|independent]] events. That this relation between <math>E</math> and <math>F</math> is symmetric may be seen more readily by realizing that it is the same as saying
 
*&Omega; is a non-empty set, sometimes called the "sample space", each of whose members is thought of as a potential outcome of a random experiment. For example, if 100 voters are to be drawn randomly from among all voters in California and asked whom they will vote for governor, then the set of all sequences of 100 Californian voters would be the sample space &Omega;.
*''F'' is a [[sigma-algebra]] of subsets of &Omega; whose members are called "events". For example the set of all sequences of 100 Californian voters in which at least 60 will vote for Schwarzenegger is identified with the "event" that at least 60 of the 100 chosen voters will so vote. To say that ''F'' is a sigma-algebra necessarily implies that the complement of any event is an event, and the union of any (finite or countably infinite) sequence of events is an event.
 
*''F'' is a [[sigma-algebra]] of subsets of &Omega; whose members are called "events". For example the set of all sequences of 100 Californian voters in which at least 60 will vote for Schwarzenegger is identified with the "event" that at least 60 of the 100 chosen voters will so vote. To say that ''F'' is a sigma-algebra necessarily implies that the complement of any event is an event, and the union of any (finite or countably infinite) sequence of events is an event.
 
*P is a probability measure on ''F'', i.e., a [[measure (mathematics)|measure]] such that P(&Omega;) = 1.
 
 
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[[Kategori:Téori probabilitas]]
 
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