Covariance: Difference between revisions

Revision as of 21:14, 11 July 2018

The covariance between two random variables $X$ and $Y$ is defined as $c o v (X, Y) = E ((X - E (X)) (Y - E (Y)))$ .

A lot of explanations of covariance say things like "if the covariance is high, then the two variables vary together, so that when one is higher than average the other is as well". That sounds more like conditional expectation though, specifically $E (Y - E (Y) ∣ X - E (X))$ . Can we express covariance in terms of this conditional language?
Explain difference (in units, range of values) with correlation. Can we get positive/negative/large/small covariance and negative/positive/small/large correlation?

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	* A lot of explanations of covariance say things like "if the covariance is high, then the two variables vary together, so that when one is higher than average the other is as well". That sounds more like conditional expectation though, specifically <math>\mathrm E(Y - \mathrm E(Y) \mid X - \mathrm E(X))</math>. Can we express covariance in terms of this conditional language?		* A lot of explanations of covariance say things like "if the covariance is high, then the two variables vary together, so that when one is higher than average the other is as well". That sounds more like conditional expectation though, specifically <math>\mathrm E(Y - \mathrm E(Y) \mid X - \mathrm E(X))</math>. Can we express covariance in terms of this conditional language?
	* Explain difference (in units, range of values) with correlation.		* Explain difference (in units, range of values) with correlation. Can we get positive/negative/large/small covariance and negative/positive/small/large correlation?