Editing E (mathematical constant) (section)

=== Stochastic representations ===
In addition to exact analytical expressions for representation of {{mvar|e}}, there are stochastic techniques for estimating {{mvar|e}}.  One such approach begins with an infinite sequence of independent random variables {{math|''X''<sub>1</sub>}}, {{math|''X''<sub>2</sub>}}..., drawn from the [[uniform distribution (continuous)|uniform distribution]] on [0, 1]. Let {{mvar|V}} be the least number {{mvar|n}} such that the sum of the first {{mvar|n}} observations exceeds 1:

:<math>V = \min\left\{ n \mid X_1 + X_2 + \cdots + X_n > 1 \right\}.</math>

Then the [[expected value]] of {{mvar|V}} is {{mvar|e}}: {{math|E(''V'') {{=}} ''e''}}.<ref>{{cite journal|last=Russell|first= K.G. |jstor=2685243 |title=Estimating the Value of e by Simulation |journal= The American Statistician|volume= 45|issue= 1|date= February 1991|pages= 66–68 |doi=10.1080/00031305.1991.10475769}}</ref><ref>Dinov, ID (2007) ''[http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_LawOfLargeNumbers#Estimating_e_using_SOCR_simulation Estimating e using SOCR simulation]'', SOCR Hands-on Activities (retrieved December 26, 2007).</ref>