Question

If X is a binomial variate with parameters n and p, where `0gt pgt` such that `(P(X=r))/(P(X=n-r))` is independent of n and r, then p equals.
A. `1//2`
B. `1//3`
C. `1//4`
D. none of these

Answer 1

Correct Answer - A
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`.