hw3[1]

hw3[1] - B (1 / 2) and if for example X 2 = 1 then X 3 ∼...

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ECE255AN Fall 2011 Homework set 2, due Thursday 10/20 Recall the typical-set definition: T n δ def = { x n : 2 - n ( H + δ ) P ( x n ) 2 - n ( H - δ ) } . 1. Let P = ( 1 2 , 1 4 , 1 8 , 1 8 ). Find the size and probability of T 4 1 / 4 . 2. Characterize all distributions where for all n 0, (a) T n 0 = T n , (b) T n 1 = T n . 3. Let X 0 = 0 and X 1 = 1, and for i 2 let X i U [ X 0 ,...,X i - 1 ]. For example X 2
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Unformatted text preview: B (1 / 2) and if for example X 2 = 1 then X 3 ∼ B (2 / 3). Show that (a) H ( X i ) = 1 for all i , (b) H ( X ) ≤ 1 2 . (c) Optional (hard): determine H ( X ). 4. Chapter 3 problems 31, 33. 5. Chapter 4 problems 4, 6, 10, 27. 1...
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This document was uploaded on 01/19/2012.

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