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
Unformatted text preview: University of Illinois Fall 2010 ECE 313: Problem Set 6: Solutions Reliability and CDFs 1. [Reliability of three s t networks] (a) Network outage occurs if and only if at least one link on the upper s t path fails and at least one link on the lower s t path fails. The probability that at least one link on the upper path fails is one minus the probability that no links on the path fail, or 1 (1 p ) 3 = 3 p 3 p 2 + p 3 . The same is true for the lower path, and the states of the two paths are independent. So P ( F ) = (3 p 3 p 2 + p 3 ) 2 . For p = 0 . 001 , P ( F ) . 0000089820 . (b) P ( D i ) = ( 4 i ) p i (1 p ) 4 i for i = 0 , 1 , 3 , 4, because the number of links from among { 1 , 2 , 3 , 4 } that fail has the binomial distribution with parameters 4 and p. P ( D 2 ,s ) = 2 p 2 (1 p ) 2 because D 2 ,s is the union of two disjoint events, each having probability p 2 (1 p ) 2 . The first of these events is that links 1 and 2 fail and links 3 and 4 do not fail, and the second of these events is that links 3 and 4 fail and links 1 and 2 do not fail. Similarly, P ( D 2 ,d ) = 4 p 2 (1 p ) 2 , because...
View
Full
Document
This note was uploaded on 02/09/2011 for the course ECE 313 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Milenkovic,O

Click to edit the document details