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Add missing normalization factor

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Martin Thoma 2016-03-27 15:09:27 +02:00
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@ -109,7 +109,7 @@
\caption{Approximations of $\Phi_{0;1}(x + \Delta x)$} \caption{Approximations of $\Phi_{0;1}(x + \Delta x)$}
\end{table} \end{table}
\begin{align*} \begin{align*}
\Phi_{0;1}(x) &= \int_{-\infty}^{x} e^{- t^2 / 2} \mathrm{d} t & \Phi_{0;1}(x) &= \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} e^{- t^2 / 2} \mathrm{d} t &
\Phi_{0;1}(1.65) &\approx 0.9505\\ \Phi_{0;1}(1.65) &\approx 0.9505\\
\Phi_{\mu; \sigma^2}(x) &= \Phi_{0;1} \left (\frac{x-\mu}{\sigma} \right ) & \Phi_{\mu; \sigma^2}(x) &= \Phi_{0;1} \left (\frac{x-\mu}{\sigma} \right ) &
\Phi_{0;1}(-x) &= 1 - \Phi_{0;1}(x) \Phi_{0;1}(-x) &= 1 - \Phi_{0;1}(x)