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

Options

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

Answer

C

Explanation

(c ) Given ,n=6 and P(X=2)=9P(X4)
`rArr " " ""^(6)C_(2)p^(2)q^(4)=9.^(6)C_(4)p^(4)q^(2)`
`rArr " " 9p^(2)=q^(2)`
`rArr " " p=(1)/(3)q`
`:.` We know that p+q=1
`rArr " " (q)/(3)+q=1 rArr q=(3)/(4)` and`p=(1)/(4)`
`:.` Variance=npq`=6.(1)/(4).(3)/(4)=(9)/(8)`