The rst component is a nonempty set each element of is

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Unformatted text preview: Bc B c c B A A Ac A A c A A B A B Figure 1.1: Karnaugh map showing how two events, A and B , partition Ω. The Axioms of Probability An experiment is modeled by a probability space, which is a triplet (Ω, F , P ). The first component, Ω, is a nonempty set. Each element ω of Ω is called an outcome and Ω is called the sample space. The second component, F , is a set of subsets of Ω called events. The final component, P , of the triplet (Ω, F , P ), is a probability measure on F , which assigns a probability, P (A), to each event A. The axioms of probability are of two types: event axioms, which are about the set of events F , and probability axioms, which are about the probability measure P. 8 CHAPTER 1. FOUNDATIONS Event axioms The set of events, F , is assumed to satisfy the following axioms: Axiom E.1 Ω is an event (i.e. Ω ∈ F ). Axiom E.2 If A is an event then Ac is an event (i.e. if A ∈ F then Ac ∈ F ). Axiom E.3 If A and B are events then A ∪ B is an event (i.e. if A, B ∈ F then A...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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