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Unformatted text preview: S07 EEE 350 Random Signal Analysis Homework 5 Solutions Feb. 20th, 2007 Problem Solutions : Yates and Goodman, 2.3.2 2.3.10 2.3.11 and 2.3.13 Problem 2.3.2 Solution (a) Each paging attempt is an independent Bernoulli trial with success probability p . The number of times K that the pager receives a message is the number of successes in n Bernoulli trials and has the binomial PMF P K ( k ) = ( n k ) p k (1- p ) n- k k = 0 , 1 , . . . , n otherwise (1) (b) Let R denote the event that the paging message was received at least once. The event R has probability P [ R ] = P [ B > 0] = 1- P [ B = 0] = 1- (1- p ) n (2) To ensure that P [ R ] ≥ . 95 requires that n ≥ ln(0 . 05) / ln(1- p ). For p = 0 . 8, we must have n ≥ 1 . 86. Thus, n = 2 pages would be necessary. Problem 2.3.10 Solution (a) We can view whether each caller knows the birthdate as a Bernoulli trial. As a result, L is the number of trials needed for 6 successes. That is, L has a Pascal PMF with parameters p = 0 . 75 and k = 6 as defined by Definition 2.8. In particular,= 6 as defined by Definition 2....
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