Sample Variance Well Known Theorem

Suppose $X_1,..,X_n{\sim }_{iid}N(\mu ,{\sigma }^2)$

• $X=\frac{1}{n}{\sum }_{i=1}^n{X}_i$ and
• $S^2=\frac{1}{n-1}{\sum }_{i=1}^n(X_i-\overline{X}{)}^2$