Variance - Unbiased Estimator: Var(B|X) = E(BB'|X)

Reckah

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\(\displaystyle \large{ var\left(\underline{\hat{\beta}}\, |\, X\right)\,=\, E\left(\underline{\hat{\beta}\hat{\beta}}'\,|\,X \right)}\)
 

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Variance - Unbiased Estimator

Hello everyone, i hope you are doing well. ;)

This is my first thread. I'm currently studying at university.

I'm stuck with this

\(\displaystyle \large{ var\left(\underline{\hat{\beta}}\, |\, X\right)\,=\, E\left(\underline{\hat{\beta}\hat{\beta}}'\,|\,X \right)}\)



we know that B^ is an unbiased estimator and is a matrix ( B^1,B^2,...,B^n)

Var(X)= E[(X-u)²] but i don't understand why B = (X-u). It has to come from the fact that B is an unbiased estimator (so E(B^) - B =0) but i don't find the mathematical explanation.

Thanks for any help.
 

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