Example questions for bias/consistent estimators.

Now, I know how to do this particular one, but I was wondering if anyone had a place to get questions similar to this? I've tried googling, but have not come up with anything.

Consider the regression model: $y=Bx + u$, where $\mathbb{E}(u)=0$, $\mathbb{Var}(u)=\sigma^2$. Is the following estimator an asymptotically unbiased estimator for $B$?

$$\mathbb{E}(B) = \frac{\mathbb{Var}(n u)}{\sigma^2 n}$$

Many thanks.

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I would expect the estimator for $B$ to be a function of $(x_i,y_i)$ pairs, given that this is a regression model. Could you please clarify the question. Also, please review my edit, to make sure the intended meaning is intact. –  Sasha May 1 '12 at 20:06
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