2nd moment about origin of the random variable X given by P then the value of 7P

X	-3	-2	-1	0	1	2	3
P(X)	5k	3k	k	k	k	2k	k

$\sum \mathrm{P}\left(\mathrm{X}={\mathrm{x}}_{\mathrm{i}}\right)=1\Rightarrow 5\mathrm{k}+3\mathrm{k}+\mathrm{k}+\mathrm{k}+\mathrm{k}+2\mathrm{k}+\mathrm{k}=1\Rightarrow 14\mathrm{k}=1$

$\Rightarrow \mathrm{k}=\frac{1}{14}\therefore 2^{\text{nd }}\text{ moment about origin }$

$\begin{array}{l}\mathrm{E}\left({\mathrm{X}}^2\right)=\sum {\mathrm{X}}_{\mathrm{i}}^2\mathrm{P}\left(\mathrm{X}={\mathrm{x}}_{\mathrm{i}}\right)=9\left(\frac{5}{14}\right)+4\left(\frac{3}{14}\right)+1\left(\frac{1}{14}\right)+0+1\left(\frac{1}{14}\right)+4\left(\frac{2}{14}\right)+9\left(\frac{1}{14}\right)\\ \\ \end{array}$

$P=\frac{76}{14}=\frac{38}{7}\Rightarrow 7P=38$