{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw-sln-05

# hw-sln-05 - S07 EEE 350 Random Signal Analysis Homework 5...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

hw-sln-05 - S07 EEE 350 Random Signal Analysis Homework 5...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online