Hey Antoine. Great to hear from you. Thanks for the analysis and link.

In the code of mine you quote, below, I would say that as one increases the number of (uniformly distributed) random variables xi, what changes is the standard deviation of what is already a Normal (or Gaussian) distribution. That is, as the number of averaged random variables increases, the tighter the clustering around the 0.5 mean.

In other words, even when we average only 2 uniformly distributed random variables, the distribution is Normal (or Gaussian). What changes is not that it gets closer to a Normal distribution but, instead, it is already a Normal distribution, and what we change is the standard deviation, the tightness of the clustering around the mean.

And I think that makes intuitive sense. If we compute the averages of a whole big bunch of uniformly distributed random variables, like a hundred of them, we will obviously almost always get a value really really close to 0.5. Whereas when we use just two random variables, as below in the first example, we are still going to get a 'bell' shaped curve over time, but there will be more frequent deviation from the 0.5 mean toward the left extremity of 0 and the right extremity of 1.


On 7/12/2018 8:49 AM, Antoine Schmitt wrote:
This method is the way to approximate a gaussian distribution.
The higher the number of additions, the closer to the gaussian distribution you get.

Le 11 juil. 2018 à 02:18, Jim Andrews <jim@vispo.com> a écrit :

For instance,

x1 = Math.random();
x2 = Math.random();
x3 = (x1 + x2)/2;

Both x1 and x2 are random nums between 0 and 1. So too is x3. But x3 has a different distribution than x1 or x2. x3 has values around 0.5 more frequently than it has values around any other number.

x1 = Math.random();
x2 = Math.random();
x3 = Math.random();
x4 = (x1 + x2 + x3)/3;

And in the above, x4 is yet more tightly clustered around 0.5

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