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post5 - STAT 511-2 Spring 2012 Lecture 5 Jun Xie 2...

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1 STAT 511-2 Spring 2012 Lecture 5 Jan 20, 2012 Jun Xie 2 Introduction of Probability Probability is a chance measurement defined on sample space and for events of a random experiment. An experiment is any activity or process whose outcome is subject to uncertainty. The sample space of an experiment, denoted by S , is the set of all possible outcomes of that experiment. Example Experiment of tossing a coin, S ={Head, Tail} Experiment of tossing a die, S ={1,2,3,4,5,6} An event is any collection (subset) of outcomes contained in the sample space. An event is simple if it consists of exactly one outcome and compound if it consists of more than one outcome. Event = Set Operations 1. Complement A’= S \A 2. Union, ? ∪ ? , “A or B” 3. Intersection, ? ∩ ? , “A and B” Example 8 Let S ={0,1,2,3,4,5,6}, A={0,1,2,3,4}, B={3,4,5,6}, C={1,3,5}. Then A’={5,6} ? ∪ ? ={0,1,2,3,4,5,6}= S ? ∪ ? ={0,1,2,3,4,5} ? ∩ ? ={3,4} ? ∩ ? ={1,3} ( ? ∩ ? ) ={0,2,4,5,6} Null event denoted by , is the event consisting of no outcomes whatsoever. When ? ∩ ? = , A and B are said to be mutually exclusive or disjoint events.

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