The probability distribution of a random variable X is given below :

 Then, Var $\left(\frac{X}{2}\right)$ is :

0.361875

The correct answer is Option (2) → 0.361875

As,

$Var(aX)=a^2\,Var(X)$

$Var(\frac{X}{2})=(\frac{1}{2})^2\,Var(X)=\frac{1}{4}\,Var(X)$

and,

$Var(X)=E(X^2)-[E(X)]$^2$

$=(0+0.25+0.6+0.6+0.6)-(0+0.25+1.2+1.8+2.4)$

$=5.05-(2.05)^2$

$=1.4475$

$∴Var(\frac{X}{2})=\frac{1}{4}×1.4475=0.361875$