Question

The mean and variance of a random variable $X$ having a binomial distribution are $4$ and $2$ respectively, find the value of $ P(X=1) $ .

• A. $ 1/4 $
• B. $ 1/16 $
• C. $ 1/8 $
• D. $ 1/32 $

Answer 1

The Correct Option is D

Given, mean, $ np=4 $ ?.(i) Variance, $ npq=2 $ ?.(ii) $ \frac{npq}{np}=\frac{2}{4} $
$ \Rightarrow $ $ q=\frac{1}{2} $
$ \therefore $ $ p=\frac{1}{2} $ From Eq (i), we get $ n=\frac{4}{1/2}=8 $ Now, $ P(X=1){{=}^{n}}{{C}_{1}}{{p}^{1}}{{q}^{n-1}} $
${{\left( \frac{1}{2} \right)}^{1}}{{\left( \frac{1}{2} \right)}^{7}}=\frac{8!}{1!7!}\times \frac{1}{{{2}^{8}}}=\frac{8}{{{2}^{8}}}=\frac{1}{32} $