MathGroup Archive: March 2009 [00108]

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How to express the results in normal cdf instead of erf()

To: mathgroup at smc.vnet.net
Subject: [mg97106] How to express the results in normal cdf instead of erf()
From: Irving Zhu <irving.zhu at gmail.com>
Date: Thu, 5 Mar 2009 04:56:27 -0500 (EST)

Hi All,

I am working on some integrals involving the Normal Distribution, and would
like the end results to be expressed in normal density as opposed to the
Erf[] function.

For example, the default result of the following:

Integrate[PDF[NormalDistribution[0, 1], x] Exp[x], x] will result in an
expression in Erf[].

I'd like it to be in terms of CDF[NormalDistribution[]] instead.

Of course the two functions are related:

CDF[NormalDistribution[0,1],x] ==1/2*(1+Erf[[x/Sqrt[2]])


Is there any way to do that?

Thanks,
Irving.

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