Given X B(n, p). If E(X) = 6, V(X) = 4.2, find n and p - Vidyadip

Question

Given $X \sim B(n, p).$ If $E(X) = 6, V(X) = 4.2,$ find $n$ and $p$

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Answer

For $X \sim B(n, p), E(X)=n p$ and $V(X)=n p q$
Given that $E(X)=6$ and $V(X)=4.2$
$ \therefore \frac{V(X)}{E(X)}=\frac{4.2}{6}$
$\therefore \frac{n p q}{n p}=0.7$
$\therefore q=0.7$
$\therefore p=1-q$
$=1-0.7$
$=0.3$
$\therefore E(X)=n p$
$=6$
$\Rightarrow n \times 0.3=6$
$=20 $

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