Question

In a meeting $70$ of the members favour and $30$ oppose a certain member is selected at random and we take $X=0$ if he opposed, and $X=1$ if he is in favour. Then variance is:

• A. $0.12$
• B. $0.21$
• C. $0.16$
• D. $1.2$

Answer 1

The correct option is B $0.21$

Given: $X=0$ if members oppose, and $X=1$ if members are in favour.
$P(X=0)=30\%=30/100=0.3$
$P(X=1)=70\%=70/100=0.7$
Hence, the required probability distribution is,
$\begin{array}{ccc}\text{X}& \text{0}& \text{1}\\ \text{P(X)}& \text{0.3}& \text{0.7}\end{array}$
Therefore $E\left(X\right)$ is:
$E\left(X\right)=\sum _{i=1}^n{x}_i{p}_i$
$=0\times 0.3+1\times 0.7\Rightarrow E\left(X\right)=0.7$
And $E\left(X^2\right)$ is
$E\left(X^2\right)={\sum }_{i=1}^n{x}_i^{2}p\left(x_i\right)=(0{)}^2\times 0.3+(1{)}^2\times 0.7\Rightarrow E\left(X^2\right)=0.7$
Then Variance, $Var\left(X\right)=E\left(X^2\right)-\left(E\right(X){)}^2=0.7-(0.7{)}^2=0.7-0.49=0.21$