# NotesSep1 - Independent Events Two events A and B are independent if P(A B = P(A)P(B or equivalently if P(A|B = P(A as long as P(B = 0 If P(B = 0

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Independent Events Two events, A and B , are independent, if P ( A B ) = P ( A ) P ( B ) , or, equivalently, if P ( A | B ) = P ( A ) as long as P ( B ) 6 = 0. If P ( B ) = 0 then A and B are always indepen- dent.

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Independence of more than 2 events 3 events Events A 1 , A 2 and A 3 are called independent if P ( A 1 A 2 ) = P ( A 1 ) P ( A 2 ) , P ( A 1 A 3 ) = P ( A 1 ) P ( A 3 ) , P ( A 2 A 3 ) = P ( A 2 ) P ( A 3 ) , P ( A 1 A 2 A 3 ) = P ( A 1 ) P ( A 2 ) P ( A 3 ) . If only the ﬁrst 3 requirements hold, then the events are called pairwise independent . There are examples of pairwise independent events that are NOT independent.
Independence of n events Events A 1 ,A 2 ,...,A n are called independent if for any selection A i 1 ,A i 2 ,...,A i k of these events P ( A i 1 A i 2 ... A i k ) = P ( A i 1 ) P ( A i 2 ) ...P ( A i k ) for k = 2 , 3 ,...,n .

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An equivalent deﬁnition is given in the text : Events A 1 ,A 2 ,...,A n are independent if P ( A 1
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## This note was uploaded on 09/20/2010 for the course OR&IE 3500 at Cornell University (Engineering School).

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NotesSep1 - Independent Events Two events A and B are independent if P(A B = P(A)P(B or equivalently if P(A|B = P(A as long as P(B = 0 If P(B = 0

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