This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 18.05 Lecture 5 February 14, 2005 2.2 Independence of events. P ( A B ) = P ( AB ) P ( B ) ;  Definition A and B are independent if P ( A B ) = P ( A )  P ( AB ) P ( A B ) = = P ( A ) P ( AB ) = P ( A ) P ( B )  P ( B ) Experiments can be physically independent (roll 1 die, then roll another die), or seem physically related and still be independent. Example: A P ( A 1 ) = { } . P ( B 2 { 1 , 3 } = P ( AB 1 3 odd , B ) = ) = , therefore independent. = = { 1, 2, 3, 4 } . Related events, but independent. .AB = 2 3 2 P ( AB ) = 1 3 2 Independence does not imply that the sets do not intersect. Disjoint = Independent. If A, B are independent, find P ( AB c ) P ( AB ) = P ( A ) P ( B ) AB c = A \ AB , as shown: so, P ( AB c ) = P ( A ) P ( AB ) = P ( A ) P ( A ) P ( B ) = P ( A )(1 P ( B )) = P ( A ) P ( B c ) therefore, A and B c are independent as well. similarly, A c and B c are independent. See Pset 3 for proof....
View
Full
Document
 Summer '06
 DrStag
 Probability

Click to edit the document details