In a meeting, $70 \%$ of the members favour and $30 \%$ oppose a certain proposal. A member is selected at random and we take $X=0$ if he opposed, and $X=1$ if he is in favour. Find $\mathrm{E}(\mathrm{X})$ and $\operatorname{Var}(\mathrm{X})$.

Home » In a meeting, of the members favour and oppose a certain proposal. A member is selected at random and we take if he opposed, and if he is in favour. Find and .

In a meeting, $70 \%$ of the members favour and $30 \%$ oppose a certain proposal. A member is selected at random and we take $X=0$ if he opposed, and $X=1$ if he is in favour. Find $\mathrm{E}(\mathrm{X})$ and $\operatorname{Var}(\mathrm{X})$ .

In a meeting, $70 \%$ of the members favour and $30 \%$ oppose a certain proposal. A member is selected at random and we take $X=0$ if he opposed, and $X=1$ if he is in favour. Find $\mathrm{E}(\mathrm{X})$ and $\operatorname{Var}(\mathrm{X})$ .

Solution:

If members are opposed, $X=0$ , and if members are in favour, $X=1$ .

$\mathrm{P}(\mathrm{X}=0)=30 \%=30 / 100=0.3$

$P(X=1)=70 \%=70 / 100=0.7$

As a result, the necessary probability distribution is,

ieret

$E(X)$ is:

$\mathrm{E}(\mathrm{X})=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}}$

$=0 \times 0.3+1 \times 0.7$

$\Rightarrow E(X)=0.7$

And $E\left(X^{2}\right)$ is:

$\mathrm{E}\left(\mathrm{X}^{2}\right)=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}^{2} \cdot \mathrm{p}\left(\mathrm{x}_{\mathrm{i}}\right)$ $=(0)^{2} \times 0.3+(1)^{2} \times 0.7$