Question

Suppose X follows a binomial distribution with parameters n and p, where 0<p<1. If $\frac{P(X=r)}{P(X=n-r)}$ is independent of n for every r, then p=

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

The correct option is A

$\frac{1}{2}$

$\frac{P(x=r)}{P(x=n-r)}=\frac{{}^n{c}_r{p}^r{q}^{n-r}}{{}^n{c}_{n-r}{p}^{n-r}{q}^r}={\left(\frac{q}{p}\right)}^{n-2r}\text{It is independent of n if}p=q=\frac{1}{2}$