# 08_23 - STAT 400 Examples for Fall 2011 Complement of A A...

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Unformatted text preview: STAT 400 Examples for 08/23/2011 Fall 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. 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 !...
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08_23 - STAT 400 Examples for Fall 2011 Complement of A A...

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