E[X]=\displaystyle\sum\limits_{i=0}^n \{i*\frac{2i-1}{n^2}\}= \displaystyle\sum\limits_{i=0}^n \frac{2i^2 - i}{n^2}= \frac{2}{n^2}\displaystyle\sum\limits_{i=0}^n i^2 - \frac{1}{n^2}\displaystyle\sum\limits_{i=0}^n i