Lecture-11

Lecture-11 - Lecture 11. Expected Value (resumed) To...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 11/29/2011 for the course MATH 3355 taught by Professor Britt during the Spring '08 term at LSU.

Page1 / 3

Lecture-11 - Lecture 11. Expected Value (resumed) To...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online