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Let X be a binomial random variable with parameters n and p, where 0<p<1. If the ratio P(X=r) / P(X=n-r) does not depend on n or r, then the value of p is

1. 1/2
2. 1/3
3. 1/4
4. none of these

Correct answer: 1/2

Solution

P(X=r)/P(X=n-r) = (p/q)^r (q/p)^(n-r) = (p/q)^(2r-n). This is independent of n and r only if p/q=1, i.e. p=1/2.

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