# 1 - 5. Random "20" questions Let X be uniformly distributed...

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5. Random “20” questions Let X be uniformly distributed over { 1 , 2 ,...,m } . Assume m = 2 n . We ask random questions: Is X S 1 ? Is X S 2 ?...until only one integer remains. All 2 m subsets S of { 1 , 2 ,...,m } are equally likely. The questions are independently and identically distributed, and subsets are drawn with replacement. (a) Firstly, how many deterministic questions would be needed to determine X ? (b) Henceforth, we generate questions randomly in the manner described above. Without loss of generality, suppose that X = 1 is the random object. What is the probability that object 2 yields the same answers for k random questions as object 1? (c) What is the expected number of objects in { 2 , 3 ,...,m } that have the same answers to k random questions as does the correct object 1? (d) Suppose we ask n + n random questions. What is the expected number of wrong objects agreeing with the answers? (e) Use Markov’s inequality Pr

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## This note was uploaded on 02/05/2012 for the course EE EE308 taught by Professor B.k.dey during the Spring '09 term at IIT Bombay.

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1 - 5. Random "20" questions Let X be uniformly distributed...

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