A discrete random variable $X$ has the distribution $B(15, p)$. Given that $\operatorname{Var}(X)=3.15$. Then, the two possible values of $p$ are

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Here, } n=15, q=1-p \ & \operatorname{Var}(X)=315 ; n p q=315 \ & \quad 15 	imes p(1-p)=315 \ & \Rightarrow \quad p-p^2=0.21 \Rightarrow p^2-p+0.21=0 \ & \Rightarrow \quad p^2-0.7 p-0.3 p+0.21=0 \ & \Rightarrow \quad p(p-0.7)-0.3(p-0.7)=0 \ & \quad p=0.7,0.3\end{aligned}$

A discrete random variable $X$ has the distribution $B(15, p)$. Given that $\operatorname{Var}(X)=3.15$.…

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