If X has binomial distribution with mean np and variance npq, then `(P(X = r))/(P(X = r - 1))` is equal to

Options

A. `1//2`
B. `1//3`
C. `1//4`
D. none of these

Answer

A

Explanation

We have ,
`(P(X=r))/(P(X=n-r))=(.^Nc_(r)p^r(1-p)^(n-r))/(.^nC_(n-r)p^(n-r)(1-p)^r)`
`rArr (P(X=r))/(P(X=n-r))==((1-p)/(p))^(n-2r)=(1-(1)/(p))^(n-2r)`
For this to be independent of n and r, we must have `1-1//p=1rArr p=1//2`.