Chebyshev's Inequality in Probability
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Chebyshev's Inequality in Probability
Chebyshev's inequality states that for any distribution, a certain amount of data must be within a stated number of standard deviations from the mean.
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SOLVED:Use Chebyshev's inequality to show that if X and Y are two arbitrary random variables satisfying E{(X-Y)^2}=0, then we have P(X=Y)=1, namely X and Y are almost surely identical. [Hint: P(|X-Y|>ϵ)=0 for any ϵ>0 .]
SOLVED:Use Chebyshev's inequality to show that if X and Y are two arbitrary random variables satisfying E{(X-Y)^2}=0, then we have P(X=Y)=1, namely X and Y are almost surely identical. [Hint: P(|X-Y|>ϵ)=0 for any ϵ>0 .]
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SOLVED:Use Chebyshev's inequality to show that if X and Y are two arbitrary random variables satisfying E{(X-Y)^2}=0, then we have P(X=Y)=1, namely X and Y are almost surely identical. [Hint: P(|X-Y|>ϵ)=0 for any ϵ>0 .]
SOLVED:Use Chebyshev's inequality to show that if X and Y …
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We saw that if we want to have a probability of at least 95% that the poll results are within 1 percentage point of the truth, Chebyshev's inequality recommends a sample size of n=50,000 . This is very large compared to what is done in practice. Newspaper polls use smaller sample sizes for various reasons. For each of the following, decide whether it is a valid reason. In the real world, a) the accuracy requirements are looser.b) the Chebyshev bound is too conservative. c) the people sampled are
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