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Expectation of Covariance Estimate 
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#1
Feb2413, 09:21 PM

P: 39

So I'm trying to take the expectation of the covariance estimate.
I'm stuck at this point. I know I have to separate the instances where i=j for the terms of the form E[XiYj], but I'm not quite sure how to in this instance. The answer at the end should be biased, and I'm trying to find a way to make it unbiased. But first tings first, I have to simplify the above. 


#2
Feb2413, 10:41 PM

P: 39

Is this the next step? What's after that if so?



#3
Feb2513, 10:00 PM

P: 4,572

Hey brojesus111 and welcome to the forums.
I think you will have to incorporate the mean terms by putting something like + X_bar  X_bar. Also given your expression, another that comes to find is try and complete the square in the way of getting E[(XX_bar)(YY_bar)] by matching this expression with the one you have been given. The difference between the two will give the bias. 


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