# lec40 - E n t r o p y 1 S e l f i n f o r m a t i o n a p p...

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Unformatted text preview: E n t r o p y 1 S e l f- i n f o r m a t i o n a p p l i e s t o a s i n g l e l e t t e r . E n t r o p y a p p l i e s t o t h e e n t i r e s e t o f l e t t e r s ( a l p h a b e t ) : H ( S ) = H ( p 1 , . . . , p n ) = − n summationdisplay i = 1 p i l o g 2 p i E n t r o p y d e p e n d s o n l y o n t h e p r o b a b i l i t i e s o f e v e n t s . E n t r o p y i s t h e a v e r a g e o f s e l f- i n f o r m a t i o n ( m e a s u r e d b y t h e a v e r a g e n u m b e r o f b i t s p e r l e t t e r ) . L e c t u r e 4 E n t r o p y 2 • H i s c o n t i n u o u s • H i s s y m m e t r i c • = H ( 1 , , . . . , ) ≤ H ( p 1 , . . . , p n ) ≤ H ( 1 n , . . . , 1 n ) = l o g 2 n • H ( p 1 , . . . , p n ) = H ( p 1 , . . . , p n , ) L e c t u r e 4 E n t r o p y 3 E x : S = { x 1 , x 2 , x 3 , x 4 , x 5 } , P = { 7 8 3 6 4 1 3 2 1 3 2 1 6 4 } − l o g 2 P = { . 1 6 8 6 . 2 7 . 1 5 6 2 . 1 5 6 2 . 9 3 8 } H ( S ) = . 7 8 1 8 O n a v e r a g e , t h e r e i s . 7 8 1 8 b...
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## This note was uploaded on 03/02/2011 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell.

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lec40 - E n t r o p y 1 S e l f i n f o r m a t i o n a p p...

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