$ \begin{array} {llllllll} \textbf{X:}& 1& 2& 3& 4 \\ \textbf{P(X):}& \large\frac{1}{10}&\large \frac{1}{5} &\large\frac{3}{10}& \large\frac{2}{5} \end{array}$

$E(X^{2})=\Large\sum p_{i}x_{i}^{2}=\frac{1}{10}\times 1+\frac{1}{5}\times 2^{2}+\frac{3}{10}\times 3^{2}+\frac{2}{5}\times 4^{2}$

$\Large\frac{1+8+27+64}{10}$

$=\Large\frac{100}{10}$

=$10$