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Unformatted text preview: Lecture 27 Outline and Examples Correlation (Ross 7.4) Markovs Inequality. Chebyshevs Inequality. (Ross 8.2) Example. Ex 4e p. 329 Let X 1 , X 2 ,..., X n be independent and identically distributed random variables having variance 2 . Show that Cov( X i X , X ) = 0 . Conclusion: The sample mean and a deviation from the sample mean are uncorrelated (i.e. if the mean is large it need not imply a large deviation). Although Cov( X , Y ) provides information about how X and Y vary jointly, it has a major shortcoming: It is not independent of the units in which X and Y are measured. Eg. if X is height and Y is weight of a person picked at random. If initially Cov( X , Y ) = 0 . 15 and measurements are in terms of m and kg, if change measurements in terms of cm, then X 1 = 100 X and Cov( X 1 , Y ) = Cov(100 X , Y ) = 100Cov( X , Y ) . Thus Cov is sensitive to units of measurement. We now define a measure of association between X and Y , independent of the scales of measurement. Correlation...
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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.
 Spring '10
 RohiniKumar
 Correlation, Variance

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