Question

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

Answer: (A)

$\frac{1}{3}$

Answer 2

Here, $n=6$
According to the question
${ }^{6} C_{2} \,p^{2} \,q^{4}=4 .^{6}\, C_{4} \,p^{4} \,q^{2}$
$\Rightarrow q^{2}-4 p^{2}$
$\Rightarrow(1-p)^{2}=4 p^{2}$
$\Rightarrow 3 p^{2}+2 p-1=0$
$\Rightarrow(p+1)(3 p-1)=0$
$\Rightarrow p=\frac{1}{3}$
$(\because p$ cannot be negative)