Question

Find the Binomial probability distribution whose mean is $3$ and variance is $2$

• A. ${(\frac{2}{3}+\frac{1}{3})}^9$
• B. ${(\frac{5}{3}+\frac{2}{3})}^9$
• C. ${(\frac{3}{3}+\frac{1}{2})}^9$
• D. None of these

Answer 1

The correct option is A ${(\frac{2}{3}+\frac{1}{3})}^9$

Mean = $np=3$

variance = $npq=2$

$np\left(q\right)=2$

$3q=2\Rightarrow q=\frac{2}{3}$

$p=1-q=1-\frac{2}{3}=\frac{1}{3}$

$\therefore n=3\times 3=9$

Hence the distribution is ${(\frac{2}{3}+\frac{1}{3})}^9$.