\begin{align*} \sigma^2 & = E[X^2] - \mu^2\\ & = \left [ 0^2 \cdot 0.10 + 1^2 \cdot 0.25 + 2^2 \cdot 0.40 + 4^2 \cdot 0.15 + 7^2 \cdot 0.10 \right ] - 2.35^2\\ & = 0 + 0.25 + 1.60 + 2.40 + 4.90 - 5.5225\\ & = 9.15 - 5.225\\ & = 3.6275 \end{align*}