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I am trying to figure out the following proof.

The third line is not clear. We all know that (a+b)^2=a^2+2ab+b^2. The term 2ab should be 0, but I can't figure out why.

I have found other proofs here on this site, but this won't leave me alone, I need to know why 2ab in this case is 0.

Thank you !

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1 Answer 1

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$E[T(X)-E(T(X))]=E(T(X))-E(T(X))=0$. (Some of your E have a $\theta$ index and some don't, but actually all of these assume $\theta$, so you can put it everywhere or leave it out everywhere.)

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