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Unformatted text preview: Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Homework 8 Solutions (Monday, May 19) Question 1: Exercise 56, § 5.4, p219. A binary communication channel transmits a sequence of “bits” (0s and 1s). Suppose that for any particular bit transmitted, there is a 10% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. a Consider transmitting 1000 bits. What is the approximate probability that at most 125 transmission errors occur? Let the transmitted sequence be t 1 , . . . , t n for t i ∈ { , 1 } and n = 1000, and let the received sequence be r 1 , . . . , r n for r i ∈ { , 1 } , and define the rvs X 1 , . . . , X n as X i = 1 ( t i 6 = r i ), i.e., each X i is Bernoulli taking value 1 wp p = 0 . 1 if there was a flip at position i , else taking value 0. Let T = X 1 + ··· + X n denote the number of errors. Note that T ∼ Bin( n, p ), and approximately...
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This note was uploaded on 06/24/2008 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.
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