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(Requires Calculus p(1−p)n\frac { p ( 1 - p ) } { n }

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(Requires calculus.)Let Y be a Bernoulli random variable with success probability Pr(Y = 1)= p. It can be shown that the variance of the success probability p is p(1−p)n\frac { p ( 1 - p ) } { n } Use calculus to show that this variance is maximized for p = 0.5.

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