Question

The mean and variance of a random variable $X$ having a binomial distribution are $4$ and $2$ respectively then $P(X=1)$ is ______

• A. $\frac{1}{16}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{1}{32}$

Answer 1

The correct option is D $\frac{1}{32}$

Mean $=np=4$

Variance$=npq=2$

$⟹q=\frac{1}{2}⟹p=\frac{1}{2}$

$n=\frac{4}{p}=8$

$P(X=1){=}^8{C}_1{p}^1{q}^{8-1}=8.\frac{1}{2}.\frac{1}{2^7}$$=\frac{1}{32}$