Q. The mean and variance of a random variable $X$ having a binomial distribution are 4 and 2 respectively, then $P(X = 1)$ is
A) $\frac{1}{32}$
B) $\frac{1}{16}$
C) $\frac{1}{8}$
D) $\frac{1}{4}$
Explanation
(a)
Given, $np = 4,\ npq = 2$
$\Rightarrow \ p = q = \frac{1}{2},\ n = 8$
We know, $P(X = r) = {\ ^{n}C}_{r}p^{r}q^{n - r}$
$\therefore\ P(X = 1) = {\ ^{8}C}_{1}\left( \frac{1}{2} \right)^{7}\left( \frac{1}{2} \right)^{1} = 8 \times \frac{1}{2^{8}} = \frac{1}{32}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.