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# PS06 - University of Illinois Fall 2009 ECE 313 Problem Set...

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University of Illinois Fall 2009 ECE 313: Problem Set 6 Bayes’ Formula and Midterm Review Problems Due: Wednesday October 7 at 4 p.m. Reading: Powerpoint Lecture Slides, Sets 13-16 Noncredit Exercises: Chapter 3: Problems 1, 2, 5, 10, 12, 16, 31, 38, 39, 51, 52 Theoretical Exercises 1, 2, 8, 16; Self-Test Problems 1-14. Reminders: No class on Wednesday September 30 and Friday October 2 but office hours as usual next week 1. [Conditional Probabilities] This is Theoretical Exercise 3.5 in Ross. We say that event B gives positive information about event A if P ( A | B ) > P ( A ), that is, the occurrence of B makes the occurrence of A more likely. Now suppose that B gives positive information about A . If so, (a) Does A give positive information about B ? (b) Does B c give negative information about A , that is, is it true that P ( A | B c ) < P ( A )? (c) Does B c give positive information or negative information about A c ? 2. [Hindsight] The probability that a light bulb manufactured by Transylvania Corp. burns out during the n -th hour of operation is p 1 ( n ), n = 1 , 2 , . . . . The probability that a light bulb manufactured by Eastinghouse Corp. burns out during the n -th hour of operation is p 2 ( n ), n = 1 , 2 , . . . . Note that we are not giving you numerical values of these probabilities but do not forget that p 1 ( n ) = p 2 ( n ) = 1. A bulb is equally likely to have been made by one of the two manufacturers. Express your answers to the following questions in terms of p 1 ( n ) and p 2 ( n ).

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PS06 - University of Illinois Fall 2009 ECE 313 Problem Set...

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