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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
An equivalent definition is given in the text : Events A 1 ,A 2 ,...,A n are independent if P ( A 1
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/20/2010 for the course OR&IE 3500 at Cornell University (Engineering School).

Page1 / 11

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online