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 of $X$ is

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

Answer 1

Answer: (A)

$\frac{1}{3}$

Here n=6

According to the question,

${}^6{C}_2{p}^2{q}^4=4{\times }^6{C}_4{p}^4{q}^2⟹q^2=4p^2⟹(1-p{)}^2=4p^2⟹3p^2+2p-1=0⟹(p+1\left)\right(3p-1)=0⟹p=\frac{1}{3},p=-1$

p cannot be negative, hence $p=\frac{1}{3}$