Normal distribution

very commonly used distribution

$mean=\mu$ $variance=\sigma^2$ $pdf(x)=\frac{1}{\sqrt{2\pi}\sigma}\mbox{ } e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

The variable $X \sim N(\mu, \sigma^2)$ is said to be normally distributed with mean and variance as $\mu$ and $\sigma^2$ . All normally distributed variables can be compared to each other by transformation to the standard normal distribution: $Z = \frac{X - \mu}{\sigma}$ where $Z \sim N(\mu, \sigma^2)$ The number of standard deviations away from the mean translates to the probability $P(Z{>}z) = 5{\%}$ when $z=1.67$ or $P(Z{>}z) = 1{\%}$ when $z=2.3$

Normal probability distribution

Code to reproduce this plot in octave:

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8 p=normpdf([-3:0.2:3],0,1);
plot(p);
title("Normal distribution");
xt2=[0,8,16,24,32];
set(gca,'XTick',xt2);
set(gca,'XTicklabel',{'-3.2','-1.6','0','1.6','3.2'});
print('npdf.ps','-dpsc2');
# convert npdf.ps -trim -resize 70% npdf.png