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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 Pollster’s 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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 Spring '10
 MuntherDahleh
 Systems Analysis, Probability, Standard Deviation, Probability theory

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