Editing Binomial distribution (section)

=== Limiting distributions ===

* ''[[Poisson limit theorem]]'': As {{math|''n''}} approaches {{math|∞}} and {{math|''p''}} approaches 0 with the product {{math|''np''}} held fixed, the {{math|Binomial(''n'', ''p'')}} distribution approaches the [[Poisson distribution]] with [[expected value]] {{math|1=''λ'' = ''np''}}.<ref name="nist"/>
* ''[[de Moivre–Laplace theorem]]'': As {{math|''n''}} approaches {{math|∞}} while {{math|''p''}} remains fixed, the distribution of
*: <math>\frac{X-np}{\sqrt{np(1-p)}}</math>
: approaches the [[normal distribution]] with expected value&nbsp;0 and [[variance]]&nbsp;1. This result is sometimes loosely stated by saying that the distribution of {{math|''X''}} is [[Asymptotic normality|asymptotically normal]] with expected value&nbsp;0 and [[variance]]&nbsp;1. This result is a specific case of the [[central limit theorem]].