01prob - EECS 501 PROBABILITY MAPPING Fall 2001 DEF: =...

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Unformatted text preview: EECS 501 PROBABILITY MAPPING Fall 2001 DEF: = sample space =set of all distinguishable outcomes of an experiment. DEF: A = event space =set of subsets of such that A is a - algebra . DEF: An Algebra = A =a set of subsets of a set such that: 1. A A and B A A B A and A B A ; 2. A A A = - A A . Closed under , , complement in . DEF: A - algebra is an algebra closed under countable number of , . NOTE: Empty set= and are always members of any algebra A , since A A A A = A A A and = A A A . NOTE: A A and B A A B A and A B = ( A B ) A . So DeMorgans law closure under and closure under . EX: Experiment: Flip a coin twice. Let H i =heads on i th flip. Sample space: = { H 1 H 2 , H 1 T 2 , T 1 H 2 , T 1 T 2 } (2 2 elements). Event space: A =power set of =set of all subsets of (2 2 2 elements). A = { , , { H 1 H 2 } , { H 1 T 2 } , { T 1 H 2 } , { T 1 , T 2 } , { H 1 } , { H 2 } , { T 1 } , { T 2 } , { H 1 H 2 }{ T 1 T 2 } , { H 1 T 2...
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This note was uploaded on 07/22/2011 for the course EECS 370 taught by Professor Lehman during the Spring '10 term at University of Florida.

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01prob - EECS 501 PROBABILITY MAPPING Fall 2001 DEF: =...

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