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Binomial Distribution — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution1 Mark
Question
Given $X \sim B(n, P)$ : If $n=10, E(X)=8$, find $\operatorname{Var}(X)$.
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Answer

Given: $n=10, E(X)=8$
$ E(X)=n p$
$8=10 p$
$p=\frac{8}{10}=\frac{4}{5}$
$q=1-p=1-\frac{4}{5}=\frac{1}{5}$
$\operatorname{Var}(X)=n p q=10\left(\frac{4}{5}\right)\left(\frac{1}{5}\right)=\frac{8}{5} $
Hence, $\operatorname{Var}(X)=\frac{8}{5}$.

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