So I'm revising my stats by doing a past exam paper, and I'm stuck on one of the questions about unbiased estimators. The question goes...

Suppose that , ,..., are a random sample from a population with mean and variance .

a)Prove that the mean estimator is unbiased for . State carefully any formulae you use.

b)Prove that has variance . State carefully any formulae you use.

It's probably really simple like the last unbiased estimator Q I posted a while back, but I'm just stumped.