| $x$ | 0 | 1 | 2 | 3 |
| $P ( X =x)$ | $\frac{1}{8}$ | $\frac{3}{8}$ | $\frac{3}{8}$ | $\frac{1}{8}$ |
| $x_i$ | $p_i$ | $p_i x_i$ | $p_i x_i^2$ |
| 0 | $1 / 8$ | 0 | 0 |
| 1 | $3 / 8$ | $3 / 8$ | $3 / 8$ |
| 2 | $3 / 8$ | $6 / 8$ | $12 / 8$ |
| 3 | $1 / 8$ | $3 / 8$ | $9 / 8$ |
| Total | $12 / 8$ | $24 / 8$= 3 |
$E(X)=\mu=\sum p_i x_i=\frac{12}{8}=\frac{3}{2}$
$\operatorname{Var}(X)=\sum_{i=1}^n p_i x_i^2-\mu^2$
$\begin{aligned} & =3-\left(\frac{3}{2}\right)^2 \\ & =3-\frac{9}{4} \\ & =\frac{3}{4} \\ & \therefore \operatorname{Var}(X)=\sigma^2=\frac{3}{4}\end{aligned}$
Standard deivation of $(X)=\sigma_x=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\left(x^2+3\right)^{\frac{3}{2}} \cdot \sin ^3 2 x \cdot 2^{x^2}$
It lies in XZ plane and makes $45^{\circ}$ with positive $Z$-axis and $|\bar{a}|=10$