Question

If $X$ is a binomial variate with the range {$a,1,2,3,4,5,6$} and $P(X=2)=4P(X=4)$, then the parameter $p$ of $X$ is

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $\frac{1}{3}$

Here, $n=6$
According to the question, we have
${}^6{C}_2{p}^2{q}^4=4{\cdot }^6{C}_4{p}^4{q}^2$
$\Rightarrow q^2=4p^2$
$\Rightarrow (1-p{)}^2=4p^2$
$\Rightarrow 3p^2+2p-1=0$
$\Rightarrow (p+1)(3p-1)=0$
$\Rightarrow p=\frac{1}{3}$
( $p$ cannot be negative)