Editing Standard deviation (section)

===Continuous random variable===
The standard deviation of a [[continuous distribution|continuous real-valued random variable]] {{mvar|X}} with [[probability density function]] {{math|{{var|p}}({{var|x}})}} is
<math display="block">\sigma = \sqrt{ \int_\mathbf{X} \left( x - \mu \right)^2\ p(x)\ {\mathrm d} x \;}\ , ~~\text{ where }~~ \mu \equiv \int_\mathbf{X} x\ p(x)\ {\mathrm d} x\ ,</math>

and where the integrals are [[definite integral]]s taken for {{mvar|x}} ranging over '''{{math|X}}''', which represents the set of possible values of the random variable&nbsp;{{mvar|X}}.

In the case of a [[parametric model|parametric family of distributions]], the standard deviation can often be expressed in terms of the parameters for the underlying distribution. For example, in the case of the [[log-normal distribution]] with parameters {{mvar|μ}} and {{math|{{var|σ}}{{sup|2}}}} for the underlying normal distribution, the standard deviation of the log-normal variable is given by the expression
<math display="block"> \sqrt{ \left(e^{\sigma^2} - 1\right)\ e^{2\mu + \sigma^2} \;} ~.</math>