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Unformatted text preview: University of Central Florida School of Electrical Engineering and Computer Science EEL-6532: Information Theory and Coding. Spring 2010 - dcm Homework 2 - due Monday February 15, 2010 Problem 1: A coin is flipped until the first head occurs. Let X denote the number of flips required. (1.1) Find the entropy of X in bits. (1.2) A random variable is drawn according to the geometric distribution with parameter p = 1 / 2, Prob( X = n ) = p (1- p ) n- 1 . Find an “efficient” sequence of Yes/No questions of the form “Is X contained in the set S?” Compare the expected number of questions required to determine X with the entropy H ( X ). Problem 2: Let p = ( p 1 ,p 2 ,...,p n ) be an n-dimensional probability vector. What is the minimum value of H ( p ) as p ranges over all possible values? Find all p which achieve this minimum. Problem 3: Let the joint probability density p XY ( x,y ) be given by: X/Y 1 1 / 3 1 / 3 1 1 / 3 Find: (3.1) H ( X ) ,H ( Y ); (3.2) H ( X | Y ) ,H ( Y | X ); (3.3)(3....
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This note was uploaded on 02/17/2012 for the course EEL 6532 taught by Professor Staff during the Spring '10 term at University of Central Florida.
- Spring '10
- Electrical Engineering