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:<math>\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2</math>
:<math>\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2</math>
where the [[expectation|expected value]] of ''X'' is E(''X'').
where the [[expectation (math)|expected value]] of ''X'' is E(''X'').
Thus the standard deviation is
Thus the standard deviation is