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Unformatted text preview: Lecture 11. Expected Value (resumed) To calculate EX , it is not necessary to treat each element of individually. Elements may be grouped according to the values of X . Suppose that B is the set of all values of X , and let [[ X = x ]] denote the event {  X ( ) = x } . Then P ( X = x ) := P ( [[ X = x ]] ) = summationdisplay [ X = x ] f ( ) Consequently, E ( X ) = summationdisplay X ( ) f ( ) = summationdisplay x B parenleftbigg summationdisplay [ X = x ] xf ( ) parenrightbigg = summationdisplay x B x parenleftBigg summationdisplay [ X = x ] f ( ) parenrightBigg = summationdisplay x B xP ( X = x ) . In fact, in many applications, we need no more detailed knowledge of the sample space than what is provided by a random variable. If the sets [[ X = x ]] happen to contain many points, then often we may clump them together to view them as the single outcome X = x without loosing any details relevant to our application. If this is possible, then thewithout loosing any details relevant to our application....
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This note was uploaded on 11/29/2011 for the course MATH 3355 taught by Professor Britt during the Spring '08 term at LSU.
 Spring '08
 Britt
 Probability

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