Lecture 02 - 1 Lecture Plan • Experiments, Outcomes and...

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Unformatted text preview: 1 Lecture Plan • Experiments, Outcomes and Events • The Axioms of Probability • Axiom consequences • Finite Sample Space. 2 Experiments, Outcomes, Sample Space, and Events Example: • Experiment: Toss a coin three times. • Outcomes: The possible outcomes are hhh,hht,hth,htt,thh,tht,tth,ttt . • Sample space: The set of all outcomes: S = { hhh,hht,hth,htt,thh,tht,tth,ttt } • Events: Are subsets of S to which we will assign probabilities. Examples of events: A at least one head: A = { hhh,hht,hth,htt,thh,tht,tth } , B the first two tosses are heads: B = { tth,ttt } An event A is said to have occurred if any outcome ω ∈ A occurs when an experiment is conducted. Suppose an experiment is done with outcome ω = tth then all events (subsets of S ) containing ω occur. 2.1 The Axioms of Probability See section 2.4 pages 69-74. In probability we are interested in assigning numbers in [0 , 1] to certain subsets of S (called events). The following axioms allow us to do this in a consistent way. A1 If A ⊂ S is an event then P ( A ) ≥ . A2 P ( S ) = 1 A3 If A 1 ,A 2 ,... are mutually exclusive events then P ( ∪ n i =1 A i ) = n X i =1 P ( A i ) for all n = 1 , 2 ,..., ∞ ....
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This note was uploaded on 06/02/2010 for the course IEOR SIEO W4150 taught by Professor Gallego during the Spring '04 term at Columbia.

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Lecture 02 - 1 Lecture Plan • Experiments, Outcomes and...

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