Question

The mean and variance of a Binomial distribution is $4$ and $3$ respectively. Find its parameters.

Answer 1

Fact: In binomial distribution, mean $=np$ and variance $=npq$

Here given $np=4$ and $npq=3$

So $q=\frac{3}{4}\Rightarrow p=1-p=\frac{1}{4}$

$np=\frac{1}{4}$

$\Rightarrow n\left(\frac{1}{4}\right)=4$

$\Rightarrow n=16$