Question

For a Binomial probability distribution $E\left(x\right)=6$ and $Var\left(x\right)=4.2$. Find $n$ and $p$.

Answer 1

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

$Var\left(x\right)-4.2=np(1-p)$

$\Rightarrow \frac{4.2}{6}=1-p$

$\Rightarrow 0.7=1-p$

$p=0.3$

$n=6/0.3=20$

$n=20$