Given $X_1, \dots , X_n$ i.i.d. and the two sample moments $M_1 = \frac{1}{n} \sum_{i = 1}^{n} X_i = \bar{X}$ and $ M_2 = \frac{1}{n} \sum_{i = 1}^{n} X_i^2$ how can I compute: $ S^2 = \frac{1}{n} \sum_{i = 1}^{n} (X_i - \bar{X})^2$ such as: $S^2 = f(M_1, M_2)$
Thank you.