MCQ
The mean and variance of a random variable $X$ having a binomial distribution are $4$ and $2$ respectively, then $P(X = 1)$ is
- ✓$1/32$
- B$1/16$
- C$1/8$
- D$1/4$
✓
Answer
Correct option: A.
$1/32$
a
(a) $\left. {\begin{array}{*{20}{c}}{np = 4}\\{npq = 2}\end{array}} \right\}\, \Rightarrow \,q = \frac{1}{2},\,p = \frac{1}{2},\,n = 8$
(a) $\left. {\begin{array}{*{20}{c}}{np = 4}\\{npq = 2}\end{array}} \right\}\, \Rightarrow \,q = \frac{1}{2},\,p = \frac{1}{2},\,n = 8$
$P\,(X = 1) = {\,^8}{C_1}\left( {\frac{1}{2}} \right)\,\,\,{\left( {\frac{1}{2}} \right)^7}$
$ = 8.\,\frac{1}{{{2^8}}} = \frac{1}{{{2^5}}} = \frac{1}{{32}}$.
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