Two fair dice are thrown simultaneously. If X denotes the number of sixes, find the mean of X.

Here X can take values $\displaystyle 0,1$ or $\displaystyle 2$ $$\left.\begin{array}{rl} \mathrm{P}(\mathrm{X} & =0)=\frac{5}{6} \times \frac{5}{6}=\frac{25}{36} \\ \mathrm{P}(\mathrm{X} & =1)=2\left(\frac{5}{6} \times \frac{1}{6}\right)=\frac{10}{36} \\ \mathrm{P}(\mathrm{X} & =2)=\frac{1}{6} \times \frac{1}{6}=\frac{1}{36} \end{array}\right\} $$