Question

Given $X\sim B(n,p)$, If $E\left(X\right)=6,\text{Var.}\left(X\right)=4.2$, find $n$ and $p$.

Answer 1

We have,

$E\left(x\right)=6$

$np=6$

$Var.\left(X\right)=4.2$

$npq=4.2$

Therefore,

$\frac{npq}{np}=\frac{4.2}{6}$

$q=0.7$

$p=1-q=0.3$

Therefore,

$n=\frac{6}{p}=\frac{6}{0.3}=20$

Hence, this is the answer.