Question

A $r.v.X\sim B(n,p)$. If values of mean and variance of $X$ are $18$ and $12$ respectively then total number of possible values of $X$ are

• A. $54$
• B. $55$
• C. $12$
• D. $18$

Answer 1

Answer: (B)

$55$

$Mean=np=18$
$Variance=npq=12$
$\frac{npq}{np}=\frac{12}{18}$
$\therefore q=\frac{2}{3}$
Now, $p=1-q=1-\frac{2}{3}$
$\therefore p=\frac{1}{3}$
Also, $np=18$
$⟹n\left(\frac{1}{3}\right)=18$
$⟹n=54$
$\therefore$ Possible values of $X$ are
$0,1,2,.....54$
$\therefore$ No. of possible values are $55$.