finalF04 - McGILL UNIVERSITY Faculty of Engineering FINAL...

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McGILL UNIVERSITY FINAL EXAMINATION Faculty of Engineering Fall 2004 ECSE 305, Section 001 (CRN 662) PROBABILITY AND RANDOM SIGNALS I DATE: Tuesday, December 21, 2004 TIME: 9:00 – 12:00 Examiner: Prof. Benoˆ ıt Champagne Associate Examiner: Prof. Yannis Psaromiligkos Signature: Signature: INSTRUCTIONS: This is a CLOSED BOOK examination. Only one (1) double-sided handwritten CRIB SHEET permitted: crib sheets con- taining photocopied material are not allowed and will be removed. Faculty standard calculator permitted ONLY. This examination paper consists of 4 printed pages, including: a cover page, 5 questions and an appendix. Ensure that you have a complete examination. Answer ALL questions. Use one or more Answer Booklets for your solutions. You MUST RETURN this examination paper. December 21, 2004 (9:00 – 12:00) 1/4
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1. A block of n 2 bits are transmitted independently over a binary communication 20 marks channel with probability of bit error at the receiver given by p . (a) Find the probability that the received block of bits contains two or more errors. (b) Find the probability that the received block contains two or more errors given that it contains at least one error. (c) Show that the probability of two or more consecutive errors (i.e., all the errors occurring in a single burst of consecutive bits) can be expressed as p n f ( q/p ) where q = 1 - p and the function f ( x ) , n - 1 l =1 lx l - 1 . 2.
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.

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finalF04 - McGILL UNIVERSITY Faculty of Engineering FINAL...

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