Suppose a random variable X follows the binomial distribution with parameters n and p, where 0

Question

Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r) / P(x = n–r) is independent of n and r, then p equals

Philoid · Accepted Answer

In binomial distribution, we know P(X=r) = ⁿC_r

where q=1-p

Therefore,

= ⁿC_r / ⁿC_r

= /

Since, ⁿC_r= ⁿC_n-r

Accorting to question, this expression is independent of n and r if

Hence, p =1/2