Suppose that constitute a random sample from a normal distribution with parameters and .

Q: Show that is a biased estimator of . Moreover, adjust to form an unbiased estimator for .

[Hint: Recall the distribution of and the result ].

A: Let . Since ~ we have that and . Furthermore, using the result in the hint and the fact that ~ we have that

.

So,

.

I am not sure what do do fro the second part of the question.

Am I doing this correctly?