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Unformatted text preview: own hat. (This is the expression that we’ll ultimately be interested in.) 3. Let’s present the outcome of the experiment in the form of an Nvector ( x 1 ,x 2 ,...,x i ,...,x N ) , where x i , i = 1 ,...,N, is the hat selected by the ith graduate. How many possible outcomes of the experiment are there? (By assumption, all outcomes are equally likely.) 4. The expression P ( E i 1 E i 2 ··· E i r ) appears in identity ( † ). Give a formula for it. What does it represent in this example? 5. Use your answer to 4 to complete the following X 1 ≤ i 1 <i 2 < ··· <i r ≤ N P ( E i 1 E i 2 ··· E i r ) = 6. Now write down an expression for P N [ i =1 E i ! = 7. Finally, using your answer to 6, write down an expression for the probability that none of the graduates selects her/his own hat. 2...
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This note was uploaded on 10/14/2010 for the course MATH 319 taught by Professor Clionagolden during the Spring '10 term at Bard College.
 Spring '10
 ClionaGolden
 Math, Statistics, Probability

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