Question

A random variable $X$ is binomially distributed with mean $12$ and variance $8$. The parameters of the distribution are ...... & .......

• A. $36,\frac{2}{3}$
• B. $36,\frac{1}{3}$
• C. $24,\frac{1}{3}$
• D. $24,\frac{2}{3}$

Answer 1

Answer: (B)

$36,\frac{1}{3}$

Mean $=\mu =np$ = 12; $n=$ number of trials ; $p=$ probability of success ; $q=(1-p)=$ probability of failure
Variance $={\sigma }^2=npq=8$
$8=np(1-p)=12(1-p)$ ;
$p=\frac{1}{3}$
$\mu =np=12$
$n=\frac{12}{p}=12\times \frac{3}{1}=36$
Parameters are $n=36$ and $p=\frac{1}{3}$