chap5-solutions - Selected Solutions for Chapter 5:...

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Selected Solutions for Chapter 5: Probabilistic Analysis and Randomized Algorithms Solution to Exercise 5.2-1 Since HIRE-ASSISTANT always hires candidate 1 , it hires exactly once if and only if no candidates other than candidate 1 are hired. This event occurs when candi- date 1 is the best candidate of the n , which occurs with probability 1=n . HIRE-ASSISTANT hires n times if each candidate is better than all those who were interviewed (and hired) before. This event occurs precisely when the list of ranks given to the algorithm is h 1; 2; : : : ; n i , which occurs with probability 1=nŠ . Solution to Exercise 5.2-4 Another way to think of the hat-check problem is that we want to determine the expected number of fixed points in a random permutation. (A fixed point of a permutation ± is a value i for which ±.i/ D i .) We could enumerate all per- mutations, count the total number of fixed points, and divide by to determine the average number of fixed points per permutation. This would be a painstak- ing process, and the answer would turn out to be 1 . We can use indicator random variables, however, to arrive at the same answer much more easily.
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This note was uploaded on 04/20/2010 for the course IE ie200 taught by Professor . during the Spring '10 term at 카이스트, 한국과학기술원.

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chap5-solutions - Selected Solutions for Chapter 5:...

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