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Standard Normal Random Variable

A continuous random variable ${\cal N}(\mu,\sigma^2)$ is defined by a density function f:

\begin{displaymath}f(z)= \phi(z)=\frac{1}{\sqrt{2 \pi}} e^{-\frac{1}{2}z^2}\end{displaymath}

Standard Normal Integrals:

\begin{displaymath}\int_{-\infty}^{+\infty}\phi(z)=1 \qquad
; \qquad \int_{-\in...
...\phi(z)=0 \qquad;
\qquad \int_{-\infty}^{+\infty}z^2\phi(z)=1 \end{displaymath}

 

Important fact:

\begin{displaymath}\Phi(x)=\int_{-\infty}^{x}\phi(z) \mbox{ is NOT available in closed form}\end{displaymath}



Susan Holmes
1998-12-07