Proving the equation

**noob mathematician** · Mar 8th 2010, 10:00 PM

Suppose we define

$S_{xy}=\sum\limits_{i=1}^N (y_i-\mu_y)(x_i-\mu_x)/(N-1)$

How do I show that $E(\overline{y}-\mu_y)(\overline{x}-\mu_x)=(1-f)S_{xy}/n$ ?

where $f=n/N$

**matheagle** · Mar 8th 2010, 10:49 PM

Originally Posted by noob mathematician

Suppose we define

$S_{xy}=\sum\limits_{i=1}^N (y_i-\mu_y)(x_i-\mu_x)/(N-1)$

How do I show that $E(\overline{y}-\mu_y)(\overline{x}-\mu_x)=(1-f)S_{xy}/n$ ?

where $f=n/N$

you can't

$E(\overline{y}-\mu_y)(\overline{x}-\mu_x)$ is a constant

while $S_{xy}$ 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?

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