An estimator of a parameter is unbiased iff:
You first problem is to determine the value of so that:
is an unbiased estimator for the variance.
This is imposible unless the variance is as the expectation of the right hand side is .
Now if instead it was meant to be:
we have:
This last bit of simplification because the are independently identically distributed.
So:
so can you now tell us what value of will make an unbiased estimator?
RonL