As we will see it is much easier to specify

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As we will see, it is much easier to specify probability models for continuous sample spaces. 8
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Given an experiement, an event is any subset of . Usually we denote events by A , B , C , and so on. EXAMPLE 1 : A 1,3,5 is the event that the number showing on the die is odd. EXAMPLE 2 : A 365,366,. ..,729,730 is the event that it takes at least one year, but not more than two, for the DJIA to pass at least 10 percent more of its current value. EXAMPLE 3 : A 0,.20 is the event that less than 20 percent of the land area is devoted to agriculture. 9
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The event space is the set of all events associated with a particular experiment. We denote the event space by . is a set whose elements are sets. Generally, we need to satisfy certain restrictions in order to have probability measures with well-defined features. (These features are subtle only in the case of a continuous sample space.) 10
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If is discrete, we can take to be the set of all subsets of . This always includes the empty set, – also called the impossible event and , also called the certain event .If is finite and contains m elements, contains 2 m elements. So, even in Example 1, where contains only six outcomes, contains 64 possible events. (For example, the event that the number on the die is at least four is 4,5,6 .) EXAMPLE 4 : Suppose an urn contains three balls, blue, green, and red. If we draw a ball at random, the sample space is  b , g , r .The event space is , b , g , r , b , g , b , r , g , r , , which has eight elements. For example, the event “not blue” is g , r . 11
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If is countably infinite then there are an infinite number of subsets of . Still, it makes sense to define to be the set of all subsets of . Special care is required in defining when is continuous; it cannot be the set of all subsets of . Later we will introduce a little measure theory to cover the continuous case. 12
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2 . Set Algebra Let be a nonempty set – the event space – and let A , B , C , and so on be subsets of . We say that A is a subset of B , written A B , if every element of A is also an element of B . The complement of A (in ), denoted A c ,is A c : A . That is, all of the points in not in A . It is easy to see that A c c A . Union : A B : A or B Intersection : A B : A and B 13
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A B A 14
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Sets A and B are disjoint ,or mutually exclusive ,if A B . Set Difference : A B A B c is the set of points in A not also in B . Facts: c  , c , A A c for any event A .
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As we will see it is much easier to specify probability...

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