Question

For a binomial variate with n = 6, if
$P(X=2)=9P(X=4),$then the variance is

• A. $\frac{8}{9}$
• B. $\frac{1}{4}$
• C. $\frac{9}{8}$
• D. $4$

Answer 1

The correct option is C $\frac{9}{8}$

$9P(X=4)=P(X=2)$
$9{}^6{C}_4{p}^4(1-p{)}^2={}^6{C}_2{p}^2(1-p{)}^4$
$9p^2=(1-p{)}^2$
$3p=(1-p)$
$4p=1$
$p=\frac{1}{4}$

Hence Variance
$=np(1-p)$

$=6\left(\frac{3}{16}\right)$

$=\frac{9}{8}$