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# PS08 - University of Illinois Fall 2009 ECE 313 Problem Set...

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University of Illinois Fall 2009 ECE 313: Problem Set 8 Independent Events; System Reliability; CDFs Due: Wednesday October 21 at 4 p.m. Reading: Ross, Chapter 3.4, 3.5, and 4.10; Powerpoint Lecture Slides, Sets 18-21 Noncredit Exercises: Chapter 3: Problems 53, 58, 59, 62, 63, 70-74, 78, 81 Theoretical Exercises 6, 7(a), 25, 26; Self-Test Problems 15-26. 1. [“I before E except after C”] Let A and B denote two mutually exclusive events that can occur on a trial of an experiment. Repeated independent trials of the experiment are carried out until either the event A or the event B occurs. What is the probability that A occurs before B does? 2. [What happens in Vegas stays in Vegas] The dice game of craps begins with the player (called the shooter ) rolling two fair dice. This is called the ﬁrst roll . If the sum is 2, 3, or 12, the shooter loses the game. If the sum is a 7 or 11, the shooter wins the game. If the sum is any of 4, 5, 6, 8, 9, 10, then the shooter has neither won nor lost (as yet). The number rolled is called the shooter’s point , and what happens next is described in parts (b) and (c) below. (a) What is the probability that the shooter wins the game on the ﬁrst roll? What is the probability that the shooter loses the game on the ﬁrst roll? What is the probability that the shooter’s point is i,i ∈ { 4 , 5 , 6 , 8 , 9 , 10 } ? We need 6 answers here for this last part, folks! (b) Suppose that the shooter’s point is

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PS08 - University of Illinois Fall 2009 ECE 313 Problem Set...

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