Unformatted text preview: d i.e., for a given accuracy d and given conFdence p , Joe wishes to select the minimum n such that P (  F − f  ≥ d ) ≤ p . ±or p = 0 . 05 and a particular value of d , Joe uses the Chebyshev inequality to conclude that n must be at least 50,000. Determine the new minimum value for n if: (a) the value of d is reduced to half of its original value. (b) the probability p is reduced to half of its original value, or p = 0 . 025. 3. Let X 1 ,X 2 ,... be a sequence of independent random variables that are uniformly distributed between 0 and 1. ±or every n , we let Y n be the median of the values of X 1 ,X 2 ,... ,X 2 n +1 . [That is, we order X 1 ,... ,X 2 n +1 in increasing order and let Y n be the ( n + 1)st element in this ordered sequence.] Show that the sequence Y n converges to 1/2, in probability. Page 1 of 1...
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 Spring '10
 MuntherDahleh
 Systems Analysis, Scalar, Probability, Probability theory, independent random variables, Probabilistic Systems Analysis, random variable esY

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