A$3$ For observations $x_1,x_2,$dots,$x_n$ with sample average $\stackrel{}{x},$ we can use hat$({)}^2=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}){)}^2$ as an estimator for the population variance ${}^2.$ What is the bias of this estimator? A: $\frac{1}{n}$ B: $-\frac{{}^2}{n}$ C: $-\frac{1}{n}$ D: $0E$:$\frac{{}^2}{n}$