Fall 2010HW02 - University of Illinois Fall 2010 ECE 313...

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University of Illinois Fall 2010 ECE 313: Problem Set 2: Solutions Discrete random variables 1. [A classification of students in a class] Set up a Karnaugh map using “F” for Facebook, “I” for iPad, and “T” for Twitter, and begin filling in entries by considering the given facts in the following order: 3 students on Facebook and having iPads are not on Twitter 2 students are on both Facebook and Twitter and have iPads 9 are on both Facebook and Twitter 12 are not on Facebook (so 18 are on Facebook); all numbers inside F can be filled in, and the sum of the other four numbers is 12) 2/3 of the students not on Facebook and without iPads are on Twitter; enter a and 2a in boxes as shown below in leftmost diagram. 2/3 of students not on Twitter don’t have iPads; Enter b for the number in F c IT c as show in the leftmost diagram, and then a + 6 = 2( b + 3) or a = 2 b. . Eliminate variable a . The situation is shown in the middle diagram, and the sum of the numbers in the top row is 12. 3 T T c T c F F c I I c T T c T c F F c I I c T T c T c F F c I I c a 6 7 2 3 2a b 6723 2b 4b b 2 4 5 1 67 2 Finally, since at least one student is neither on Twitter nor on Facebook, 2 b + b > 0 or b > 0 . There are only 12 students total not on Facebook, so b = 1 . The final diagram is shown on the right. Two students are not on Twitter or Facebook and don’t have iPads.
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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.

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Fall 2010HW02 - University of Illinois Fall 2010 ECE 313...

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