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I haven't taken statistics yet, but as a matter of interest I was contemplating the fact that uniform random variables added together seem to generate "bell curve" like distributions.

My question is if I add up an infinite number of equally distributed random variables will the resulting values be the normal/Gaussian distribution?

Or, perhaps will the effect of adding so many variables just cause the peak of the distribution to become excessively amplified until the function is just like one sudden spike at the center of the distribution?

What's the real behavior?

Furthermore, since brown noise is a sum of deviations from the current position (i.e. random variables) I wonder if brown noise could be considered to be normal/Gaussian noise.

Also, I've read online about something called "white Gaussian noise". What is it? How does it differ from non-white Gaussian noise? Is brown noise "Gaussian noise"? Is noise generated directly from a Gaussian curve (rather than from a random walk) what they call "white Gaussian noise"?

Thank you for your time.

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# What does an infinite sum of uniform random variables yield?

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