Question

If $X$ is binomial variate with $E\left(X\right)=5$ and variance $4$. The parameters of the distribution are

• A. $\frac{1}{4},20$
• B. $\frac{1}{5},20$
• C. $25,\frac{1}{5}$
• D. $\frac{1}{25},\frac{1}{5}$

Answer 1

The correct option is C $25,\frac{1}{5}$

Mean $=E\left(X\right)=\mu =np$ $=5$; $n$ = number of trials ; $p=$ probability of success ; $q=(1-p)=$ probability of failure
Variance $={\sigma }^2=npq=4$
$4=np(1-p)=5(1-p)$ ;
$p=\frac{1}{5}$
$\mu =np$ = 5
$n=\frac{5}{p}=5\times \frac{5}{1}=25$
Parameters are $n=25$ and $p=\frac{1}{5}$