01_21 - STAT 400 Examples for 01/21/2011 Complement of A...

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STAT 400 Examples for 01/21/2011 Spring 2011 Complement of A A ' ( not A , A , A c ) contains all elements that are not in A Intersection of A and B A B ( A and B , A B ) contains all elements that are in A and in B Union of A and B A B ( A or B ) contains all elements that are either in A or in B or both Axiom 1 Let A be any event defined over S. Then P ( A ) 0. Axiom 2 P ( S ) = 1. Axiom 3 If A 1 , A 2 , A 3 , … are events and A i A j = for each i j , then P ( A 1 A 2 A k ) = P ( A 1 ) + P ( A 2 ) + … + P ( A k ) for each positive integer k , and P ( A 1 A 2 A 3 ) = P ( A 1 ) + P ( A 2 ) + P ( A 3 ) + … for an infinite, but countable, number of events.
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Theorem 1 . P ( A ' ) = 1 – P ( A ) . Theorem 2 . P ( ) = 0. Theorem 3 . If A B, then P ( A ) P ( B ) . Theorem 4 . For any event A, P ( A ) 1. ! For any event A, 0 P(A) 1 ! P(S) = 1
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This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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01_21 - STAT 400 Examples for 01/21/2011 Complement of A...

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