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Math Help - Proving the equation

  1. #1
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    Proving the equation

    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
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by noob mathematician View Post
    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?
    Last edited by matheagle; March 8th 2010 at 11:20 PM.
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