This a past paper question I would just like to know what would be the best way to answer to get full marks. Just as it says 'briefly' you never know how little or much to write!

a) Suppose we can estimate a parameter theta using an esitmate theta^ based on a random sample of data X1,...,Xn, and suppose that for n={1,2,...}, theta^ is unbiased. Briefly explain why theta^ must be asympototically unbiased as an estimator for theta.

b) Briefly explain why an asymptotically unbiased estimator theta^ for theta is not necessarily unbiased for any finite sample size n, and give an example of an estimator for a parameter which is asymptotically unbiased, while not being unbiased for any fixed n.