The mean and variance of a random variable X having a binomial di… - Vidyadip

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) $\left. {\begin{array}{*{20}{c}}{np = 4}\\{npq = 2}\end{array}} \right\}\, \Rightarrow \,q = \frac{1}{2},\,p = \frac{1}{2},\,n = 8$

$P\,(X = 1) = {\,^8}{C_1}\left( {\frac{1}{2}} \right)\,\,\,{\left( {\frac{1}{2}} \right)^7}$

$ = 8.\,\frac{1}{{{2^8}}} = \frac{1}{{{2^5}}} = \frac{1}{{32}}$.

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