Suppose X has a binomial distribution with parameters n & p. For what p is var(X) maximized if we assumed n is fixed?
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var(X)=np(1-p)=-np^2+np
If we plot a p-var(X) graph instead of xy graph, it resembles an inverted parabola with maximum turning point at p=-n/(-2n)=1/2, hence the answer.
Hope it's correct and helpful :)
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