Suppose we define $\displaystyle S_{xy}=\sum\limits_{i=1}^N (y_i-\mu_y)(x_i-\mu_x)/(N-1)$ How do I show that $\displaystyle E(\overline{y}-\mu_y)(\overline{x}-\mu_x)=(1-f)S_{xy}/n$ ? where $\displaystyle f=n/N$
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Originally Posted by noob mathematician Suppose we define $\displaystyle S_{xy}=\sum\limits_{i=1}^N (y_i-\mu_y)(x_i-\mu_x)/(N-1)$ How do I show that $\displaystyle E(\overline{y}-\mu_y)(\overline{x}-\mu_x)=(1-f)S_{xy}/n$ ? where $\displaystyle f=n/N$ you can't $\displaystyle E(\overline{y}-\mu_y)(\overline{x}-\mu_x)$ is a constant while $\displaystyle S_{xy}$ is a rv My guess is that you're mixing up population means (mu's) and sample means (x bar's) or is that Expectation a sum?
Last edited by matheagle; Mar 8th 2010 at 11:20 PM.
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