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DHB10

Member

Registered: 2012-01-21

Posts: 2

An Integral Equation Proof Question

Please help with the proof of the following definite integral equation

∫x(Ф(x))^3 φ(x)dx=-3(1+2a/π) /(8√π)   from minus infinite to plus infinite   

where Ф(x)=∫1/√2π exp(- t^2/2) dt from minus infinite to x
φ(x)=1/√2π exp(- x^2/2)   
a=arcsin(1/3)

To be exact, φ(x) is the probability density function of standard normal distribution, Ф(x) is the cumulative probability function of standard normal distribution.

Please see the attached image for clear equation about the question.

Last edited by DHB10 (2012-01-21 01:43:05)