AKA The Normal distribution. The statistical distribution. Its importance flows from the fact that :
  • Any sum of Normal distributed variables is itself a Normal distributed variable
  • Sums of variables that, individually, are not Normal distributed tend to become Normal distributed (asymptotically)
You won't find many stochastic variables on this planet that are not Gaussian of nature.
  • The number of single girls in a bar (when measuring eg. every day at noon in the same bar
  • The number of cars passing a point on the highway (go ahead: Spend an hour a day - a 1000 days in a row and see the nice distribution curve smoothing more and more until it is perfectly Gaussian
  • The height of Japanese people
  • The number of bytes/links/images on a homepage (this one would be easy to check
Let Z be a Gaussian distributed stochastic variable with mean=0 and standard deviation=1.
    Interesting values of Z follow:
  • Prob(|Z|>=1) <= 0.3173105
  • Prob(|Z|>=1.96) <= 0.0499957
  • Prob(|Z|>=3.29055) <= 0.0010000
For the not so much into mathematics reader:
The small list shows that the probability of finding a value in the data set that is more than 3.29055 times higher than the standard deviation is 1 in a thousand. So - if all cars on the highway are doing 50 plus/minus 10, only one car in a thousand will do more/less than 50+10*3.29055 which is about 83. (Or to use the first entry in the list: The chance that there are more single girls in a bar than normally is 31.7%/2= 15.8% - go push your luck!) Well folks - that's all for now. Thanks for letting me use this place as a test stage for my thesis, where I'm actually discussing small uninteresting matters like this (focusing a little less on single girls, though)

And to ariels - yes - you're absolutely right. You'd also never find a car going faster than the speed of light, even though it SHOULD happen de temps en temps if the velocities were truly Gaussian distributed. Forgive my engineer-geekish way of looking at things (eg. 0.98 is not close to 1, it IS 1)