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W9-slides3

# W9-slides3 - Lecture 27 Outline and Examples...

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Lecture 27- Outline and Examples Correlation (Ross § 7.4) Markov’s Inequality. Chebyshev’s Inequality. (Ross § 8.2)

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Example. Ex 4e p. 329 Let X 1 , X 2 , . . . , X n be independent and identically distributed random variables having variance σ 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.

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Correlation Definition. The correlation of two random variables X and Y , denoted by ρ (
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W9-slides3 - Lecture 27 Outline and Examples...

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