I have been given two variance (S^2) estimators, S1 and S2. I am not including the square (^2) as it may cause confusion. And I am to determine the bias of these estimators. Now, given that estimator S1 has the same equation as sample variance, it should therefore be classed as 'Unbiased'. However, estimator S2 on the other hand has an equation which differs to S1, and has been proven to be bias (please correct me if i'm wrong).

The issues that I am facing are that given that I am to calculate the bias of both estimators S1 and S2, I would state that S1 has a bias of 0. However, when calculating the mean [E(S1)] and subtracting it from the population variance [Var.P], which is the formula for calculating bias of an estimator (as shown in the attachment), I do not obtain a result = 0. E.g. the population variance was something along the lines of 120, and the estimator S1 = 120.087627... Therefore does this mean that the estimator S1 is bias, even though the formula is unbias? Also, if the estimator is classed as Unbiased, then in order to calculate the bias of Estimator S2, do I proceed with [E(S2) - Var.P] or with [E(S2) - E(S1)] since S1 in this case is unbias and approx equal to Var.P

Any help would be much appreciated. Thanks