In a meeting $60 \%$ of the members favour and $40 \%$ oppose a certain proposal. A member is selected at…
In a meeting $60 \%$ of the members favour and $40 \%$ oppose a certain proposal. A member is selected at random and we take $\mathrm{X}=0$ if the opposed and $\mathrm{X}=1$ if he is in favour, then Var $\mathrm{X}=$
0.36
0.24
0.6
0.06
Solution
$\text { From the given data, we write }$
$\text { Variance }=\Sigma \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-\left(\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\right)^2=0.6-(0.6)^2=0.6-0.36=0.24$
$\text { Variance }=\Sigma \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-\left(\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\right)^2=0.6-(0.6)^2=0.6-0.36=0.24$