Finding Standard Deviation of Continous Distribution

Question

$X_1, X_2, X_3, X_4$ are continuous Uniform(0, 1) distributions.

$S_4 = X_1 + X_2 + X_3 + X_4$

Find $SD(S_4)$

Answer should be $\frac{1}{\sqrt{3}}$

Answer 1

Formula of variance should be

$$\mathbb{E}(X^2)-\mathbb{E}(X)^\color{red}{2}$$

Hence you shall end up with

$$\sqrt{\sum_{i=1}^4\left( \frac13-\frac14\right)}=\sqrt{4 \cdot \frac1{12}}=\frac1{\sqrt3}$$