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Unformatted text preview: to see a sequence of independent, equally likely 0s and 1s. Problem 7: Let X , Y and Z be three discrete random variables. Using Jensens inequality, or otherwise (e.g., the chain rule), show that I ( X,Y ; Z ) I ( Y ; Z ). When does the equality hold? Problem 8: Let X 1 , X 2 be discrete random variables drawn according to probability mass functions p 1 ( ) and p 2 ( ) over the respective alphabets X 1 = { 1 , 2 ,... ,m } and X 2 = { m + 1 , 2 ,... ,n } . Let X = b X 1 with probability X 2 with probability 1 1 Find H ( X ) in terms of H ( X 1 ) and H ( X 2 ) and . Hint: dene a function of X as : = f ( X ) = b 1 when X = X 1 2 when X = X 2 and use H ( X, ). 2...
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This note was uploaded on 10/10/2010 for the course ECE 6605 taught by Professor Staff during the Fall '08 term at Georgia Institute of Technology.
 Fall '08
 Staff

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