Hi, if someone could take a look through and help me on this problem it would me much appreciated.

Note all the following distributions have sample size 9.

Let and .

We then form the following distributions:

In each of the above cases work out the sampling distribution of the estimator, explain whether it's unbiased and give the standard error.

Here's what I've managed to do so far:

Using the fact that , and with a sample size of 9, we can then get the sampling distributions of the 3 estimators:

I think these are right, please correct me if I've made a mistake somewhere.

Now the standard error of the estimator is , giving us

SE

SE

SE

I think this is correct up to here. The only thing I'm really stuck on is how to find whether they are biased or unbiased?

Thanks in advance

Craig