WUSTL ESE 523 - exam196 (3 pages)

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exam196



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exam196

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Pages:
3
School:
Washington University in St. Louis
Course:
Ese 523 - Information Theory
Information Theory Documents

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EE 553 Fall 1996 October 17 1996 EE 553 EXAM 1 This is a closed book closed notes exam scheduled to last 90 minutes Calculators and computers are not allowed NAME Score 1 2 3 4 5 Total 1 10 points Prove that 0 7 log 0 7 0 3 log 0 3 0 2 log 0 2 0 8 log 0 8 2 0 75 log 0 75 0 25 log 0 25 You must do this without using a calculator that is without computing any of the logarithms indicated using the theoretical tools developed in this class Try to give some details to convince me that you know what you are doing 2 50 points In many sporting events such as the National League Championship Baseball Series going on now involving our very own St Louis Cardinals the teams compete in several games with the first team winning K games declared the winner of the series Note that this implies a maximum of 2K 1 games Such series are often called a best K out of 2K 1 series For example the Cardinals and Braves will play the seventh game of their best 4 out of 7 series this evening EE 553 2 Exam 1 For each of the parts of this question assume that the outcomes of all games are described by a 1 or a 0 depending on whether team one wins or loses Assume that the outcomes of all games are independent and identically distributed with P outcome 1 p a For a best 2 out of 3 series find a good lower bound on the average number of bits needed to describe the outcomes of all games played Note that we are considering the set of outcomes of all games played in a series as the random variable b Suppose that p 0 4 Find a Huffman code to describe the outcomes of all games played in a best 2 out of 3 series Find the expected codeword length c We now change the random variable definition slightly Suppose that at the end of a series we only care how many games each team won in a best 2 out of 3 series Thus if team one wins the series then team one wins two games and the other team wins either zero games or one game The random variable describing the series is then the pair l m where l denotes the



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