midterm2005

# midterm2005 - Principles of Digital Communications EPFL...

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Unformatted text preview: Principles of Digital Communications EPFL Summer Semester 2005 Prof. Rudiger Urbanke April 27, 2005 Midterm There are 9 pages. If you need any extra pages do not forget to mark your name! You have 1 hour 45 minutes. It is not necessarily expected that you finish all problems. Do not loose too much time on each problem but try to collect as many points as possible. Closed-book, no calculators, cell-phones, crypt sheet or stolen glances to your neighbors are allowed. Write what is relevant to the question! Good Luck!! Name: Ex I / 25 Ex II / 15 Ex III / 15 Ex IV / 15 Total / 70 1 I. Dice Tossing [25 points] You have two dices, one fair and one loaded ( truqu e ). A friend told you that the loaded dice produces a 6 with probability 1 4 , and the other values with uniform probabilities. You do not know a priori which one is fair or which one is loaded. You pick with uniform probabilities one of the two dices, and perform N consecutive tosses ( lanc es ) with the dice you have chosen. Let Y = ( Y 1 , ,Y N ) be the sequence of numbers observed....
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midterm2005 - Principles of Digital Communications EPFL...

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