Given X B(n, P) : If n=25, E(X)=10, find p and SD(X). - Vidyadip

Question

Given $X \sim B(n, P)$ : If $n=25, E(X)=10$, find $p$ and $\operatorname{SD}(X)$.

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Answer

Given: $n=25, E(X)=10$
$ E(X)=n p$
$10=25 p$
$p=\frac{10}{25}=\frac{2}{5}$
$\therefore q=1-p=1-\frac{2}{5}=\frac{3}{5}$
$\operatorname{Var}(X)=n p q=25 \times \frac{2}{5} \times \frac{3}{5}=6$
$\therefore S D(X)=\sqrt{ } \operatorname{Var}(X)=\sqrt{ } 6$
$\text { Hence, } p=\frac{2}{5} \text { and } S \cdot D \cdot(X)=\sqrt{ } 6 . $

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