The probability distribution of a random variable X is given below :
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 |
Then, Var $\left(\frac{X}{2}\right)$ is :
Answer & explanation
Correct answer: option 2
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$
$=(0+0.25+0.6+0.6+0.6)-(0+0.25+1.2+1.8+2.4)$
$=5.05-(2.05)^2$
$=1.4475$
$∴Var(\frac{X}{2})=\frac{1}{4}×1.4475=0.361875$