For a binomial variate X with n=6, if `P(X=2)=9,P(X=4)`, then its variance is

Options

A. `(8)/(9)`
B. `(1)/(4)`
C. `(9)/(8)`
D. `4`

Answer

C

Explanation

Given, n=6 and
`P(X=2)=9,P(X=4)`
`implies.^(6)C_(2)p^(2)q^(4)=9.^(6)C_(4)p^(4)q^(2)`
`implies9p^(2)=q^(2)impliesp=(1)/(3)q`
`because` We know that, `p+q=1`
`implies(q)/(3)+q=1impliesq=(3)/(4)`
and `p=(1)/(4)`
and `p=(1)/(4)`
`therefore` Variance=npq
`=6*(1)/(4)*(3)/(4)=(9)/(8)`