Question

If $X$ is a binomial variate with the range {$0,1,2,3,4,5,6$} and $P(X=2)=4P(X=4)$, then the parameter $p$ of $X$ is :

• A. $1/3$
• B. $1/2$
• C. $2/3$
• D. $3/4$

Answer 1

The correct option is A $1/3$

According to the problem

where, $n=6$

let us consider the problem

${}^6{C}_2{P}^2{Q}^4={4.}^6{C}_4{P}^4{C}^2$

$Q^2=4P^2$

$(1-P{)}^2=4P^2$

$3P^2+2P-1=0$

$(P+1)(3P-1)=0$

Hence,

$P=\frac{1}{3}$ and $P=-1$

But $P$ can not be negative

Therefore, the answer is $P=\frac{1}{3}$