Editing E (mathematical constant) (section)

=== Standard normal distribution ===
{{Main|Normal distribution}}

The normal distribution with zero mean and unit standard deviation is known as the ''standard normal distribution'',{{r|openstax}} given by the [[probability density function]]<!--{{r|nordistr}}-->
<math display="block"> \phi(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} x^2}. </math>

The constraint of unit standard deviation (and thus also unit variance) results in the {{frac2|1|2}} in the exponent, and the constraint of unit total area under the curve <math>\phi(x)</math> results in the factor <math>\textstyle 1/\sqrt{2\pi}</math>. This function is symmetric around {{math|1=''x'' = 0}}, where it attains its maximum value <math>\textstyle 1/\sqrt{2\pi}</math>, and has [[inflection point]]s at {{math|1=''x'' = ±1}}.