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Probability Integral


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ProbabilityIntegral
ProbabilityIntegralReIm
ProbabilityIntegralContours
alpha(x)=1/(sqrt(2pi))int_(-x)^xe^(-t^2/2)dt
(1)
=sqrt(2/pi)int_0^xe^(-t^2/2)dt
(2)
=2Phi(x)
(3)
=erf(x/(sqrt(2))),
(4)

wherePhi(x) is thenormal distribution function anderf is the error function.


See also

Erf,NormalDistribution Function

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Cite this as:

Weisstein, Eric W. "Probability Integral."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/ProbabilityIntegral.html

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Created, developed and nurtured by Eric Weisstein at Wolfram Research

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