$\text { The variance of the following probability distribution is, }$
- $\frac{1}{8}$
- $\frac{5}{8}$
- $\frac{1}{4}$
- $\frac{3}{8}$
Solution
$\begin{aligned}
& \text { Variance }=\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-\left(\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\right)^2 \\
& =\frac{5}{8}-\left(\frac{1}{2}\right)^2=\frac{5}{8}-\frac{1}{4}=\frac{3}{8}
\end{aligned}$Asked in: MHT CET 2021 (20 Sep Shift 2)