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Solving equation involving error function and normal distribution

Let $\phi(x)$ be a normal distribution, that is $\phi=\frac{1}{\sigma}\phi(x|\mu,\sigma^2)$ and $\Phi(x)$ be the CDF of $\phi$, i.e., $\Phi(x|\mu,\sigma^2)=\frac{1}{2}[1+erf(\frac{x-\mu}{\sqrt{2}\...
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