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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- Mar 8th 2010, 10:00 PMnoob mathematicianProving the equation
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 $\displaystyle f=n/N$ - Mar 8th 2010, 10:49 PMmatheagle