Révisi nurutkeun 23 Méi 2016 10.42 édit Ilhambot (obrolan \| kontribusi) Bot 20.027 suntingan m Ngarapihkeun éjahan, replaced: rea → réa (3), ngarupakeun → mangrupa (2), yen → yén (3) using AWB ← Éditan saméméhna		Révisi nurutkeun 3 Pébruari 2017 11.21 édit bolaykeun Ilhambot (obrolan \| kontribusi) Bot 20.027 suntingan m Ngarapihkeun éjahan, replaced: ea → éa (5), eo → éo Éditan salajengna →
Baris ka-2: Dina [[tiori probabiliti]], keur nyebutkeun yén dua [[event (probability theory)\|kajadian]] '''independent''' atawa '''mandiri''' dumasar kana pamikiran nu gampang yén pangaweruh kana ayana hiji kajadian lain disababkeun ku ayana pangaruh kamungkinan tina hiji kajadian sejenna. Upamana, keur meunang angka "1" dina sakali ngalungkeun dadu sarta meunang deui angka "1" dina alungan dadu kadua mangrupa conto kajadian mandiri. Hal nu sarupa, waktu urang nyebutkeun dua [[variabel acak]] bebas, we intuitively ~~mean~~méan that knowing something about the value of one of them does not yield any information about the value of the other. For example, the number ~~appearing~~appéaring on the upward face of a die the first time it is thrown and that ~~appearing~~appéaring the second time are independent. == Kajadian bebas == Baris ka-10: :<math>P(A\mid B)=P(A).</math> There are at ~~least~~léast two réasons why this statement is not taken to be the definition of independence: (1) the two events ''A'' and ''B'' do not play symmetrical roles in this statement, and (2) problems arise with this statement when events of probability 0 are involved. When one recalls that the conditional probability P(''A'' \| ''B'') is given by Baris ka-38: Two random variables ''X'' and ''Y'' are independent iff for any numbers ''a'' and ''b'' the events [''X'' ≤ ''a''] and [''Y'' ∈ ''b''] are independent events as defined above. Similarly an arbitrary collection of random variables—possible more than just two of them—is independent precisely if for any finite collection ''X''<sub>1</sub>, ..., ''X''<sub>''n''</sub> and any finite set of numbers ''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub>, the events [''X''<sub>1</sub> ≤ ''a''<sub>1</sub>], ..., [''X''<sub>''n''</sub> ≤ ''a''<sub>''n''</sub>] are independent events as defined above. The ~~measure~~méasure-~~theoretically~~théoretically inclined may prefer to substitute events [''X'' ∈ ''A''] for events [''X'' ≤ ''a''] in the above definition, where ''A'' is any [[Borel algebra\|Borel set]]. That definition is exactly equivalant to the one above when the values of the random variables are [[real number]]s. It has the advantage of working also for complex-valued random variables or for random variables taking values in any [[topological space]]. Lamun ''X'' sarta ''Y'' bebas, mangka [[nilai ekspektasi\|operator ekspektasi]] ''E'' mibanda sipat nu hade

Kamandirian statistik: Béda antarrépisi