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Unformatted text preview: with the following sequence of PMFs: Does converge? What is ? Convergence of the Sample Mean (finite mean and variance ) i.i.d., Mean: Variance: Chebyshev : Limit: The Pollsters Problem : fraction of population that do . person polled: : fraction of Yes in our sample. Suppose we want: Chebyshev: But we have : Thus: So, let (conservative). Die Experiment (1) Unfair die, with probability of face . Independent throws: Thus, are i.i.d. with PMF: Define: Let: frequency of face Die Experiment (2) is Bernoulli with probability , thus: Then: Chebyshev: It follows that: Therefore, the sample frequency of each face converges in probability to the probability of that face. This allows us to do simulations....
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This note was uploaded on 12/08/2010 for the course MATH 6.041 / 6. taught by Professor Muntherdahleh during the Spring '10 term at MIT.
 Spring '10
 MuntherDahleh
 Systems Analysis, Probability

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